Post on 06-Apr-2022
1
Geometry Resource Book
Name _____________________ Period _____
Room #219
2
Geometry Symbols Geometry Marks
∠ angle
congruent segments
arc (“arc AC”)
congruent angles
≅ congruent
(∠G≅ ∠S or 𝐴𝐵 ≅ 𝐶𝐷)
parallel
= equal (2 + 3 = 5)
perpendicular (or right angle)
𝑃𝑅 line
𝐴𝐵 line segment or segment
m∠R or m𝐴𝐵
measure (m∠R = “measure of angle
R” or m𝐴𝐵 = “measure of
segment AB”)
∥or//parallel
(𝐴𝐵 ∥ 𝐶𝐷)
⊥ perpendicular (𝐴𝐵 ⊥ 𝐶𝐷)
𝑍𝑌 ray ~ similar Δ triangle
Vocabulary: 180º, 360º, a
3
Geometry Vocabulary
Section Word Picture Definition
How to write it
with symbols
How to say it
1.3 180º angle
also called a “straight angle”
1.3 360º angle
a full turn around a circle
1.3 acute angle
an angle with a measure less than 90º
is acute.
“Angle R is acute.”
1.5 acute triangle
a triangle in which all of the angles have a
measure less than 90º
ΔABC is acute.
“Triangle ABC is acute.”
3.3 altitude (of a triangle)
a segment from a vertex of a triangle perpendicular to the opposite side or the line containing the
opposite side
€
∠R
Vocabulary: a
4
Section Word Picture Definition
How to write it
with symbols
How to say it
1.2 angle
made by two rays that have the same
endpoint
∠1 ∠𝐸
not ∠𝐷 not ∠𝐹
not ∠𝐷𝐸 not ∠𝐷𝐹 ∠𝐷𝐸𝐹 ∠𝐹𝐸𝐷
not ∠𝐸𝐷𝐹 not ∠𝐷𝐹𝐸
“Angle 1” “Angle E”
“Angle DEF”
“Angle FED”
1.2 angle bisector
a ray that divides an angle into two
congruent angles
∠ABD≅∠CBD
“Angle ABD is
congruent to angle CBD.”
1.6 arc (of a circle)
two points on a circle and the part of the
circle between them
“Arc AB”
1.6 arc measure
equal to the measure of the central angle
that goes with the arc m =
85°
“The measure of arc AB is
85 degrees.”
Vocabulary: b
5
Section Word Picture Definition
How to write it
with symbols
How to say it
1.5
base angles of an
isosceles triangle
• the two angles opposite the two sides that are congruent in an isosceles triangle
• the two angles on both ends of the base of an isosceles triangle
∠A and ∠C are the
base angles of ΔABC.
“Angle A and angle C are the
base angles of triangle ABC.”
10.1 base of a solid
•
1.5 base of an isosceles triangle
the side of an isosceles triangle that
is not congruent to either of the other
sides
𝐴𝐶 is the base of ΔABC.
“Segment AC is the base of ΔABC.”
1.1 bisect
divides into two congruent parts
B is the bisector of
“point B is the
bisector of segment
DC”
€
DC
Vocabulary: c
6
Section Word Picture Definition
How to write it
with symbols
How to say it
1.6 central angle
an angle with its vertex at
the center of a circle
is a central angle of circle O.
“Angle BOC is a central
angle of circle O.”
1.6 chord
a segment whose endpoints are on a circle
is a chord of circle A.
“Segment DC is a chord of
circle A.”
1.6 circle
• all the points that are the same distance from a point (that point is the center of the circle)
• has an arc measure of 360º
circle O “circle O”
6.5 circum-ference
the distance around the
outside of a circle
1.1 collinear
points that are on the same line
(“co” = together, “linear” = line)
A, B, and C are
collinear
“points A, B and C
are collinear”
1.3 comple-mentary angles
two angles whose sum is 90º
35º + 55º = 90º
“35 plus 55 equals
90”
€
∠BOC
€
DC
Vocabulary: c
7
Section Word Picture Definition
How to write it
with symbols
How to say it
1.4 concave polygon
• has one or more interior angles greater than 180º
• looks like a vertex has been pushed into the polygon
opposite of convex polygon
1.6 concentric circles
circles with the same center
1.8 cone
1.2 congruent angles
two angles that have the same measure ∠G≅ ∠S
“Angle G is
congruent to angle
S.”
1.4 congruent polygons
two polygons that have the same sides as each other and the same angles as each
other
ABCD ≅ HGFE
Quadri-lateral
ABCD is congruent
to quadrilateral HGFE
1.1 congruent segments
segments that have the same length
𝐴𝐵≅ 𝐶𝐷
“Segment AB is
congruent to segment
CD.”
Vocabulary: c
8
Section Word Picture Definition
How to write it
with symbols
How to say it
2.1 conjecture
a hypothesis or educated guess, a statement which appears to be true but has not been proven
1.4 consecutive angles
• two angles at the ends of the same side
• two angles that are next to each other in a polygon
• “consecutive” means “in a row” or “one after the other”
∠A and ∠E are
consecu-tive angles
1.4 consecutive sides
• two sides that are the sides of the same angle
• two sides that are next to each other in a polygon
• “consecutive” means “in a row” or “one after the other”
𝐴𝐵 and 𝐴𝐸 are consecu-tive sides
1.4 consecutive vertices
• two vertices that are the ends of the same side
• two vertices that are next to each other in a polygon
• “consecutive” means “in a row” or “one after the other”
A and E are
consecu-tive
vertices
1.4 convex polygon
• all the interior angles are less than 180º
• all of the vertices are pushing out, away from the center
• opposite of concave polygon
Vocabulary: c, d
9
Section Word Picture Definition
How to write it
with symbols
How to say it
1.1 coplanar
on the same plane (“co” = together, “planar” = plane)
D, E, and F are
coplanar
“Points D, E, and F
are coplanar.”
3.7 concurrent
three or more points that intersect at a
single point
1.3 counter-example
an example that shows that something
is NOT true
1.8 cylinder
1.4 decagon
a polygon with 10 sides
2.2 deductive reasoning
Example: If Iqra is a student at South, then Iqra must be in 9th, 10th, 11th, or 12th grade. (It is a fact that South is a high school and only has students grades 9-
12.)
showing that a statement is true
because of ageed-upon assumptions or
facts
1.2 degree
the unit we use for measuring an angle
155º
155 degrees
Vocabulary: d, e
10
Section Word Picture Definition
How to write it
with symbols
How to say it
1.4 diagonal
• a segment connecting two non-consecutive vertices of a polygon
• a diagonal CAN be horizontal or vertical
𝐴𝐶 and 𝐵𝐷 are
diagonals of ABCD.
Segment AC and segment BD are
diagonals of
quadrilateral ABCD
1.6 diameter
a line segment going through the center of
a circle with its endpoints on the
circle
𝐴𝐵 is a diameter of circle
C.
“Segment AB is a diameter of circle
C.”
1.4 dodecagon
a polygon with 12 sides
1.1 endpoint
a point at the end of a line segment or a ray
A and D are the
endpoints of .
“Points A and D are
the endpoints
of segment AD.”
1.4 equiangular polygon
a polygon in which all the angles are
congruent
1.4 equilateral polygon
a polygon in which all the sides are
congruent
€
AD
Vocabulary: e, f, g, h, i
11
Section Word Picture Definition
How to write it
with symbols
How to say it
1.5 equilateral triangle
a triangle with three congruent sides
𝐴𝐵 ≅ 𝐵𝐶≅ 𝐴𝐶
4.3 exterior angle
an angle on the outside of a polygon, formed by extending a side of the polygon
∠4 is an exterior angle of ∆PQR
“Angle 4 is an
exterior angle of triangle PQR.”
1.8 hemisphere
1.4 hexagon
a polygon with 6 sides
2.1 inductive reasoning
example: All forms of life that we know of need water to survive. If we discover a new form of life, it will probably need water to survive. example:
The next picture in the sequence is:
making a conclusion based on a pattern
Vocabulary: l
12
Section Word Picture Definition
How to write it
with symbols
How to say it
1.1 intersect
two lines intersect if meet at a single point
“Line NA and line
FP intersect at point C.”
1.5 isosceles triangle
a triangle with two congruent sides
“Segment AB is
congruent to segment
BC.”
1.5 kite
a quadrilateral with two different pairs of congruent sides that
are consecutive
“Segment AB is
congruent to segment
BC. Segment
AD is congruent to segment
CD.”
9.1 leg (of a
right triangle)
the two sides of a right triangle that
make the right angle, also the two shorter
sides of a right triangle
“Segment AC and segment
CB are the legs of right
triangle ABC.”
€
AB≅BC
€
AB≅BC
€
AD ≅CD
Vocabulary: l
13
Section Word Picture Definition
How to write it
with symbols
How to say it
4.2 leg (of a an isosceles triangle)
the two congruent sides of an isosceles
triangle
“Sides AB and BC are the legs of triangle ABC.”
1.1 line
is straight, has no thickness, and goes in
both directions forever
𝑃𝑅 𝑅𝑃 𝑃𝑄 𝑄𝑃 𝑄𝑅 m
not 𝑄 not 𝑃𝑄𝑅
Line PR Line RP Line PQ Line QP Line QR Line m
1.1 line segment (or segment)
straight and has no thickness like a line,
but has two endpoints
𝐴𝐶 𝐶𝐴
not 𝐵 not 𝐴𝐵 not 𝐵𝐴 not 𝐵𝐶
not 𝐴𝐵𝐶
line segment AC (or
segment AC) line
segment CA (or
segment CA)
1.3 linear pair
a pair of angles that share a vertex and a side and their non-shared side makes a
line
∠𝐷𝐴𝐶 and ∠𝐵𝐴𝐶 are
a linear pair.
Vocabulary: m
14
Section Word Picture Definition
How to write it
with symbols
How to say it
1.6 major arc
• an arc of a circle that is larger than a semicircle
• an arc of a circle with a measure greater than 180°
is a major
arc.
“Arc AKB is a major
arc.”
1.1 measure of a segment
the length of a segment
AB = 5 cm or
m𝐴𝐵 = 5 cm
“AB equals 5 cm” or
“the measure of
segment AB is 5
cm.”
1.2 measure of an angle
the number of degrees needed to
rotate to get from one side of the angle to
the other
m∠R =
155º
“The measure of angle R is
155 degrees.”
3.2 median (of a triangle)
the segment connecting the vertex
of a triangle to the midpoint of the opposite side
𝐽𝐾 is a median of ∆KLM.
“Segment JK is a
median of triangle KLM.”
1.1 midpoint
the point on a segment that is the same distance from
both endpoints
“Segment JK is
congruent to segment
KL.”
UYAS 1
midpoint formula
formula: 𝑥! + 𝑥!2 ,
𝑦! + 𝑦!2
=3+ 52 ,
4+−22
=82 ,22
= (4, 1)
The midpoint of 𝑀𝑁 is (4 , 1).
€
JK ≅KL
Vocabulary: m, n, o
15
Section Word Picture Definition
How to write it
with symbols
How to say it
3.2 midsegment
(of a triangle)
a segment connecting the midpoint of one side of a triangle to
the midpoint of another side of the
triangle
𝐵𝐷 is a midsegme
nt of ∆ACD.
“Segment BD is a
midsegment of
triangle ACD.”
1.6 minor arc
• an arc of a circle that is smaller than a semicircle
• an arc of a circle with a measure less than 180°
is a minor arc.
“Arc AB is a minor
arc.”
1.4 n-gon
• a polygon with n sides
• n is a variable so the polygon can have any number of sides
1.4 nonagon
a polygon with 9 sides
1.3 obtuse angle
an angle with a measure of more than
90º
1.5 obtuse triangle
a triangle with one obtuse angle
m A > 90°
“the measure of angle A is
greater than 90
degrees” €
∠
Vocabulary: o, p
16
Section Word Picture Definition
How to write it
with symbols
How to say it
1.4 octagon
a polygon with 8 sides
1.3 parallel
lines that are always the same distance apart and never
intersect 𝐴𝐵//𝑀𝑁
“Line AB is parallel
to line MN.”
1.5 parallel-ogram
a quadrilateral with two pairs of parallel
sides
Segment AB is
parallel to segment
CD. Segment
AD is parallel to segment
BC.
1.4 pentagon
a polygon with 5 sides
1.4 perimeter
the total distance around the outside of
a polygon
perimeter of DCAB = 5 + 14 + 11 + 17 =
47 cm
€
AB//CD
€
AD//BC
Vocabulary: p
17
Section Word Picture Definition
How to write it
with symbols
How to say it
1.3 perpen-dicular
or
lines that intersect at 90 degree angles 𝐴𝐵 ⊥ 𝐶𝐷
Segment AB is
perpendic-ular to line
CD.
3.2 perpen-dicular bisector
a line that is perpendicular to and
bisects a segment
𝐴𝐵 ⊥ 𝐶𝐷 and
𝐴𝐷 ≅ 𝐵𝐷
“Segment AB is
perpendic-ular to line
CD and segment AD is
congruent to segment
BD.”
1.1 plane
a flat two-dimensional surface that goes on forever
M (written with an
upper-case cursive letter)
“Plane M”
1.1 point
an exact place or location B “Point B”
1.6 point of tangency
the point where a tangent touches a
circle
is tangent to circle A
and B is a point of
tangency.
“Line CD is tangent to circle A and point
B is a point of
tangency.”
€
CD
Vocabulary: p
18
Section Word Picture Definition
How to write it
with symbols
How to say it
1.4 polygon
a shape with 3 or more sides
1.8 prism
1.2 protractor
a tool for measuring angles
1.8 pyramid
Vocabulary: q, r
19
Section Word Picture Definition
How to write it
with symbols
How to say it
1.4 quadrilateral
a polygon with four sides
DGMT DTMG TMBD GMTD
not MTGD not DGTM not TMDG
“quadrilateral
DGMT” “quadrilate
ral DTMG”
1.6 radius
• a segment from the center of a circle to a point on the edge of the circle
• radius has an unusual plural – we say “one radius”, but “three radii”
is a radius of circle O.
“Segment AO is a radius of circle O.”
1.1 ray
a part of a line that starts at a point and goes forever in one
direction
𝑍𝑌 𝑍𝑋
not 𝑋𝑌 not 𝑌𝑍 not 𝑌𝑍
not 𝑍𝑋𝑌
“ray ZY” “ray ZX”
1.5 rectangle
a quadrilateral with four congruent angles
Rectangle ABCD
“Rectangle ABCD”
1.4 regular polygon
a polygon that has all congruent sides
(equilateral) and all congruent angles
(equiangular)
€
AO
Vocabulary: r, s
20
Section Word Picture Definition
How to write it
with symbols
How to say it
1.5 rhombus
a quadrilateral with all congruent sides
(equilateral)
1.3 right angle
an angle with a measure of 90º
1.5 right triangle
a triangle with one right angle
1.5 scalene triangle
a triangle in which none of the sides are
congruent
1.1 segment same as “line segment”
1.6 semicircle
• half a circle • has an arc
measure of 180º
is a semicircle
.
“Arc ABC is a
semicircle.”
1.4 side of a polygon
a line segment that is part of a polygon
Polygon ABCDE
has 5 sides. For example
one of the sides is 𝐶𝐷.
Vocabulary: s, t
21
Section Word Picture Definition
How to write it
with symbols
How to say it
1.2 sides (of an angle)
the two rays that make an angle
The sides of
are 𝐵𝐴 and
𝐵𝐶.
“The sides of angle CBA are ray BA
and ray BC.”
1.3 skew lines
lines that are not parallel, but never
intersect either
𝑃𝑆 and 𝑅𝑌 are
skew lines
1.8 space all the points in three dimensions (3-D)
1.8 sphere
1.5 square
an equilateral and equiangular quadrilateral
Square ABCD
“Square ABCD”
1.3 supple-mentary angles
a pair of angles whose sum is 180º
45º + 135º = 180º
120º + 60º = 180º
1.6 tangent
a line that intersects a circle at only one
point
is a tangent of circle O.
“Line EF is a
tangent of circle O.”
€
∠CBA
€
EF
Vocabulary: t, u, v
22
Section Word Picture Definition
How to write it
with symbols
How to say it
2.6 transversal
a line that intersects two or more other
lines
t is a transversal
.
“Line t is a transversal
.”
1.5 trapezoid
a quadrilateral with two parallel sides
(and not more than two parallel sides)
Trapezoid TRAP
“Trapezoid TRAP”
1.4 triangle
a polygon with three sides
ΔABC ΔCBA ΔBAC
Triangle ABC
12.1 trig-onometry
the study of relationships between the sides and angles
of triangles (“trigono” = triangle, “metry” = measure)
1.4 undecagon
a polygon with 11 sides
1.4 vertex (of a polygon)
• where the sides of a polygon meet
• the plural of vertex is VERTICES (for example 3 vertices)
the polygon
has 5 vertices,
named A, B, C, D,
and E
23
Section Word Picture Definition
How to write it
with symbols
How to say it
1.2 vertex (of an angle)
• the point where the two sides of an angle meet
• the plural of vertex is VERTICES (for example, 3 vertices)
B is the vertex of ∠𝐴𝐵𝐶.
“B is the vertex of
angle ABC.”
1.5
vertex angle of an
isosceles triangle
the angle between the two congruent sides
of an isosceles triangle
∠𝐴𝐵𝐶 is the vertex angle of ΔABC.
“Angle ABC is the
vertex angle of triangle ABC.”
1.3 vertical angles
the angles opposite each other when two
lines cross
∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
24
Geometry Conjectures 2.5 C-1 Linear Pair Conjecture: If two angles form
a linear pair, then ______________________.
If then
2.5 C-2 Vertical Angles Conjecture: If two angles are vertical angles, then ______________________.
If then
2.6 C-3a Corresponding Angles Conjecture (CA Conjecture): If two parallel lines are cut by a transversal, then corresponding angles are ______________.
If then
2.6 C-3b Alternate Interior Angles Conjecture (AIA Conjecture): If two parallel lines are cut by a transversal, then alternate interior angles are ______________.
If then
2.6 C-3c Alternate Exterior Angles Conjecture (AEA Conjecture): If two parallel lines are cut by a transversal, then alternate exterior angles are ______________.
If then
2.6 C-3 Parallel Lines Conjecture: If two parallel lines are cut by a transversal, then corresponding angles are ______________, alternate interior angles are ______________, and alternate exterior angles are ______________.
If then
25
2.6 C-4 Converse of the Parallel Lines Conjecture: If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are ______________________.
If then
or
or
3.2 C-5 Perpendicular Bisector Conjecture: If a point ( ) is on the perpendicular bisector of a segment, then it is _______________________ from the endpoints.
If then
3.2 C-6 Converse of the Perpendicular Bisector Conjecture: If a point is equidistant from the endpoints of a segment, then it is on the ______________________ of the segment.
If then
3.3 C-7 Shortest Distance Conjecture: The shortest distance from a point to a line is measured along the ______________________ from the point to the line.
If then
26
3.4 C-8 Angle Bisector Conjecture: If a point is on the bisector of an angle, then it is ______________________ from the sides of the angle.
If then
UYAS 3 Parallel Slope Property: In a coordinate plane, two distinct lines are parallel if and only if ________________________.
If then
UYAS 3 Perpendicular Slope Property: In a coordinate plane, two nonvertical lines are perpendicular if and only if _________________________________________________.
If then
3.7 C-9 Angle Bisector Concurrency Conjecture: The three angle bisectors of a triangle
______________________.
If then
27
3.7 C-10 Perpendicular Bisector Concurrency Conjecture: The three perpendicular bisectors of a triangle ______________________.
If then
3.7 C-11 Altitude Concurrency Conjecture: The three altitudes (or the lines containing the altitudes) of a
triangle ______________________.
If then
3.7 C-12 Circumcenter Conjecture: The circumcenter of a triangle _____________________.
If then
28
3.7 C-13 Incenter Conjecture: The incenter of a triangle ______________________.
If then
3.8 C-14 Median Concurrency Conjecture: The three medians of a triangle _____________________.
If then
3.8 C-15 Centroid Conjecture: The centroid of a triangle divides each median into two parts so that the
distance from the centroid to the vertex is _____________________ the distance from the centroid to the midpoint of the opposite side.
If then
29
3.9 C-16 Center of Gravity Conjecture: The ___________________ of a triangle is the center of gravity of the triangular region.
If then
4.1 C-17 Triangle Sum Conjecture: The sum of the measures of the angles in every triangle is _____________________.
If then
4.1 C-18 Third Angle Conjecture: If two angles of one triangle are equal in measure to two angles of
another triangle, then the third angle in each triangle ______________________.
If then
4.2 C-19 Isosceles Triangle Conjecture: If a triangle
is isosceles, then ______________________.
If then
4.2 C-20 Converse of the Isosceles Triangle Conjecture: If a triangle has two congruent angles, then _____________________.
If then
30
4.3 C-21 Triangle Inequality Conjecture: The sum of the lengths of any two sides of a triangle is _______________________ the length of the third side.
If then If then
4.3 C-22 Side-Angle Inequality Conjecture: In a triangle, if one side is longer than another side, then the
angle opposite the longer side is ______________________. If then
largest middle small
sides
angles
4.3 C-23 Triangle Exterior Angle Conjecture: The
measure of an exterior angle of a triangle ______________________.
If then
4.4 C-24 SSS Congruence Conjecture: If the three sides of one triangle are congruent to the three sides of another triangle, then ______________________.
If then
31
4.4 C-25 SAS Congruence Conjecture: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then ______________________.
If then
4.4 NOT A CONJECTURE!
If then
4.5 NOT A CONJECTURE!
If then
4.5 C-26 ASA Congruence Conjecture: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then ______________________.
If then
32
4.5 C-27 SAA Congruence Conjecture: If two angles and a non-included side of one triangle are congruent to the corresponding angles and side of another triangle, then ______________________.
If then
4.6 Corresponding parts of congruent triangles are congruent. (CPCTC)
If then
4.8 C-28 Vertex Angle Bisector Conjecture: In an
isosceles triangle, the bisector of the vertex angle is also _______________________ and ___________________.
If then
4.8 C-29 Equilateral/Equiangular Triangle Conjecture: Every equilateral triangle is ______________________, and, conversely, every equiangular triangle is ______________________.
If then
If then
≅ ∠_____≅ ∠_____ and _____ ≅______ because _________________.
33
5.1 C-30 Quadrilateral Sum Conjecture: The sum of the measures of the four angles of any quadrilateral is ______________________.
If then
5.1 C-31 Pentagon Sum Conjecture: The sum of the measure of the five angles of any pentagon is ______________________.
If then
5.1 C-32 Polygon Sum Conjecture: The sum of the
measures of the n interior angles of an n-gon is ______________________.
If then
5.2 C-33 Exterior Angle Sum Conjecture: For any polygon, the sum of the measures of a set of exterior angles is ______________________.
If then
5.2 C-34 Equiangular Polygon Conjecture: You can
find the measure of each interior angle of an equiangular n-gon by using either of these formulas:
_______________________ or
____________________.
If then
5.3 Vocabulary for kites
• Vertex angles • Nonvertex angles
34
5.3 C-35 Kite Angles Conjecture: The _______________________ angles of a kite are ______________________.
If then
5.3 C-36 Kite Diagonals Conjecture: The diagonals of a kite are ______________________.
If then
5.3 C-37 Kite Diagonal Bisector Conjecture: The diagonal connecting the vertex angles of a kite is the _______________________ of the other diagonal.
If then
5.3 C-38 Kite Angle Bisector Conjecture: The _______________________ angles of a kite are _______________________ by a __________________.
If then
5.3 Vocabulary for trapezoids
• Bases • Pair of base angles
5.3 C-39 Trapezoid Consecutive Angles Conjecture: The consecutive angles between the bases of a trapezoid are ______________________.
If then
35
5.3 C-40 Isosceles Trapezoid Conjecture: The base angles of an isosceles trapezoid are ______________________.
If then
5.3 C-41 Isosceles Trapezoid Diagonals Conjecture: The diagonals of an isosceles trapezoid are ______________________.
If then
5.4 C-42 Three Midsegments Conjecture: The three midsegments of a triangle divide it into ______________________.
If then
5.4 C-43 Triangle Midsegment Conjecture: A midsegment of a triangle is _______________________ to the third side and _______________________ the length of ______________________.
If then
5.4 C-44 Trapezoid Midsegment Conjecture: The midsegment of a trapezoid is _____________________ to the bases and is equal in length to ______________________.
If then
5.5 C-45 Parallelogram Opposite Angles Conjecture: The opposite angles of a parallelogram are ______________________.
If then
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5.5 C-46 Parallelogram Consecutive Angles Conjecture: The consecutive angles of a parallelogram are ______________________.
If then
5.5 C-47 Parallelogram Opposite Sides Conjecture: The opposite sides of a parallelogram are ______________________.
If then
5.5 C-48 Parallelogram Diagonals Conjecture: The diagonals of a parallelogram ______________________.
If then
5.6 C-49 Double-Edged Straightedge Conjecture: If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a ______________________.
If then
5.6 C-50 Rhombus Diagonals Conjecture: The diagonals of a rhombus are _____________________, and they _____________________.
If then
5.6 C-51 Rhombus Angles Conjecture: The _______________________ of a rhombus _______________________ the angles of the rhombus.
If then
37
5.6 C-52 Rectangle Diagonals Conjecture: The diagonals of a rectangle are ____________________ and _________________.
If then
5.6 C-53 Square Diagonals Conjecture: The diagonals of a square are _______________________, _______________________, and __________________.
If then
6.1 definitions:
central angle arc measure If then
6.1 C-54 Chord Central Angles Conjecture: If two chords in a circle are congruent, then they determine two central angles that are ______________.
If then
6.1 C-55 Chord Arcs Conjecture: If two chords in a
circle are congruent, then their _________________________ are congruent.
If then
6.1 C-56 Perpendicular to a Chord Conjecture: The perpendicular from the center of a circle to a chord is the __________________ of the chord.
If then
82º
38
6.1 C-57 Chord Distance to Center Conjecture: Two congruent chords in a circle are _______________________ from the center of the circle.
If then
6.1 C-58 Perpendicular Bisector of a Chord Conjecture: The perpendicular bisector of a chord ___________________ _________________________.
If then
6.2 C-59 Tangent Conjecture: A tangent to a circle _________________________ the radius drawn to the point of tangency.
If then
6.2 C-60 Tangent Segments Conjecture: Tangent segments to a circle from a point outside the circle are __________________.
If then
6.3 examples of central angles
6.3 examples of inscribed angles
39
6.3 C-61 Inscribed Angle Conjecture: The measure of an angle inscribed in a circle is ________________________.
If then
6.3 C-62 Inscribed Angles Intercepting Arcs Conjecture: Inscribed angles that intercept the same arc ______________________.
If then
6.3 C-63 Angles Inscribed in a Semicircle Conjecture: Angles inscribed in a semicircle ________________________.
If then
6.3 C-64 Cyclic Quadrilateral Conjecture: The ____________ angles of a cyclic quadrilateral are ______________________.
If then
40
6.3 C-65 Parallel Lines Intercepted Arcs Conjecture: Parallel lines intercept _________________ arcs on a circle.
If then
6.5 C-66 Circumference Conjecture: If C is the circumference and d is the diameter of a circle, then there is a number π such that C = _________________. If d = 2r where r is the radius, then C = _________________.
If then
If then
6.6 Vocabulary for arcs
• Arc measure • Arc length
6.6 C-67 Arc Length Conjecture: The length of an arc equals the ________________________.
If then
41
7.1 C-68 Reflection Line Conjecture: The line of reflection is the _________________________ of every segment joining a point in the original figure with its image.
7.2 C-69 Coordinate Transformations Conjecture: The ordered pair rule (x, y) → (−x, y) is a ______________ over the __________. The ordered pair rule (x, y) → (x, −y) is a ______________ over the __________. The ordered pair rule (x, y) → (−x, −y) is a ____________ about _____________. The ordered pair rule (x, y) → (y, x) is a ______________ over _______________.
7.2 C-70 Minimal Path Conjecture: If points A and
B are on one side of line ℓ, then the minimal path from point A to line ℓ to point B is found by ______________ _________________________.
7.3 C-71 Reflections over Parallel Lines Conjecture: A composition of two reflections over two parallel lines is equivalent to a single _________________. In addition, the distance from any point to its second image under the two reflections is ___________ the distance between the parallel lines.
7.3 C-72 Reflections over Intersecting Lines Conjecture: A composition of two reflections over a pair of intersecting lines is equivalent to a single ____________________. The angle of _________________ is ___________ the acute angle between the pair of intersecting reflection lines.
7.5 C-73 Tessellating Triangles Conjecture: ___________ triangle will create a monohedral tessellation.
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7.5 C-74 Tessellating Quadrilaterals Conjecture: __________________ quadrilateral will create a monohedral tessellation.
8.1 C-75 Rectangle Area Conjecture: The area of a rectangle is given by the formula _________________, where A is the area, b is the length of the base, and h is the height of the rectangle.
If then
If then
8.1 C-76 Parallelogram Area Conjecture: The area of a parallelogram is given by the formula _________________, where A is the area, b is the length of the base, and h is the height of the parallelogram.
If then
8.2 C-77 Triangle Area Conjecture: The area of a triangle is given by the formula ____________________, where A is the area, b is the length of the base, and h is the height of the triangle.
If then
43
8.2 C-78 Trapezoid Area Conjecture: The area of a trapezoid is given by the formula
_________________________, where A is the area, b1 and b2 are the lengths of the two bases, and h is the height of the trapezoid.
If then
8.2 C-79 Kite Area Conjecture: The area of a kite is given by the formula __________________, where d1 and d2 are the lengths of the diagonals.
If then
8.4 C-80 Regular Polygon Area Conjecture: The area of a regular polygon is given by the
formula ________________, where A is the area, a is the apothem, s is the length of each side, and n is the number of sides. The length of each side times the number of sides is the perimeter P, so sn = P. Thus you can also write the formula for area as ________________________.
If then
8.5 C-81 Circle Area Conjecture: The area of a circle is given by the formula __________________, where A is the area and r is the radius of the circle.
If then
If then
44
8.6 Area of a sector of a circle
8.6 Area of a segment of a circle
8.6 Area of an annulus of a circle
8.7
8.7 Surface Area of a Cylinder
If then
45
8.7 Surface Area of a Cone
If then
9.1 Vocabulary for right triangles
9.1 C-82 The Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. If a and b are the lengths of the legs, and c is the length of the hypotenuse, then _________________________.
If then
If then
9.2 C-83 Converse of the Pythagorean Theorem: If the lengths of the three sides of a triangle satisfy the Pythagorean equation, then the triangle ________________________.
If then
and
46
9.3 C-84 Isosceles Right Triangle Conjecture: In an isosceles right triangle, if the legs have length l, then the hypotenuse has length __________. If then
If then
If then
9.3 C-85 30°-60°-90° Triangle Conjecture: In a 30°-60°-90° triangle, if the shorter leg has length a, then the longer leg has length ___________, and the hypotenuse has length _____________.
If then
If then
If then
9.5 C-86 Distance Formula: The distance between points ( )1 1,A x y and ( )2 2,B x y is given by AB = ____________________________.
If then
9.5 C-87: Equation of a Circle The equation of a circle with radius r and center (h, k) is ________________________.
If then
the equation for the circle is
47
10.2 C-88 Prism-Cylinder Volume Conjecture: The volume of a prism or a cylinder is the ______________________ multiplied by the ______________.
If then
If then
10.3 C-89 Pyramid-Cone Volume Conjecture: If B is the area of the base of a pyramid or a cone and H is the height of the solid, then the formula for the volume is V = ____________.
If then
If then
10.6 C-90 Sphere Volume Conjecture: The volume of a sphere with radius r is given by the formula ________________________.
If then
10.7 C-91 Sphere Surface Area Conjecture: The surface area, S, of a sphere with radius r is given by the formula _____________________.
If then
48
11.1 C-92 Dilation Similarity Conjecture: If one polygon is the image of another polygon under a dilation, then _________________________.
If then
11.2 C-93 AA Similarity Conjecture: If ________ angles of one triangle are congruent to _________ angles of another triangle, then _____________ _________________.
If then
11.2 C-94 SSS Similarity Conjecture: If the three sides of one triangle are proportional to the three sides of another triangle, then the two triangles are ________________.
If then
11.2 C-95 SAS Similarity Conjecture: If two sides of one triangle are proportional to two sides of another triangle and _______________________, then the ____________________.
If then
49
11.4 C-96 Proportional Parts Conjecture: If two triangles are similar, then the corresponding __________________, ____________________, and _________________________ are ______________________ to the corresponding sides.
If then
11.4 C-97 Angle Bisector/Opposite Side Conjecture: A bisector of an angle in a triangle divides the opposite side into two segments whose lengths are in the same ratio as ________________________.
If then
11.5 C-98 Proportional Areas Conjecture: If corresponding sides of two similar polygons or the radii of two circles
compare in the ratio mn
,then their areas
compare in the ratio __________________.
If then
11.5 C-99 Proportional Volumes Conjecture: If corresponding edges (or radii, or heights) of two similar solids compare in the ratio mn
, then their volumes compare in the
ratio __________________. If then
50
11.6 C-100 Parallel/Proportionality Conjecture: If a line parallel to one side of a triangle passes through the other two sides, then it divides the other two sides ___________________. Conversely, if a line cuts two sides of a triangle proportionally, then it is ___________ to the third side.
If then
AND If then
11.6 C-101 Extended Parallel/Proportionality Conjecture: If two or more lines pass through two sides of a triangle parallel to the third side, then they divide the two sides ____________________.
If then
12.1 Labeling the Sides a Right Triangle
12.1 Definitions of Trigonometric Ratios
51
12.2 Inverse Trigonometric Ratios
12.3 C-102 SAS Triangle Area Conjecture: The area of a triangle is given by the formula
_________________________, where a and b are the lengths of two sides and C is the angle between them.
If then
12.3 C-103 Law of Sines: For a triangle with angles A, B, and C and sides of lengths a, b, and c (a opposite
A, b opposite B, and c opposite C), ________________________.
If then
52
12.4 C-104 Pythagorean Identity: For any angle A, ______________________________________________.
If then
12.4 C-105 Law of Cosines: For any triangle with sides of lengths a, b, and c, and with C the angle opposite
the side with length c ________________________.
If then