A

B

Q

P

H

T M

M

B

T M

T M P

D

1.1 Building Blocks of Geometry

Name Definition Picture Short Rorm

Point A location in space

The point P

Line

An infinite number of points extending in two directions. A

line only has length.

TM

Ray

An infinite number of points in a straight line from a given

point.

TM

Line Segment

An infinite number of points in a straight line between two

given points.

TM

Plane

A flat surface that extends outward forever with length and width, but no thickness.

Collinear points Points on the same line

Just say it

Coplanar points Points on the same plane

Just say it

Angle

Two noncollinear rays sharing the same endpoint form an

angle

BHM� or MHB� or H�

Endpoints

A terminating or starting point of a ray, line segment,

or arc Just say it 1. Name each picture using the proper notation/symbols. If you can name the picture more than one way, then do so.

B M

P H

B A

2. Draw RA , HB , g� , and a plane containing the points JML. 3. For the following picture is the notation B� a good idea? Why? 4. Use your ruler to measure the following segment in cm and then in inches and write it in the form mAB= 5. How many points define a line, a plane? 1.2 Pool Room Math. 1. Label each angle with a letter and measure the angles using a protractor. Write your answers in the form �Am

B A

C D

E

C D

B E

A

B A

C D

E

7106

9060

90

�

�

�

EBABCE

CEBmAEBmCm

D

D

D

Congruence is where two shapes have the exact same size and shape. The symbol is # Congruent segments have the exact same measure. Congruent angles have the exact same measure. *Numbers are EQUAL. *Shapes are CONGRUENT

Labeling angles and segments

Showing congruent segments and angles.

BA �#�

DC �#� BEAE # DECE # CDAB #

x What would be wrong with using the notation E� ? Mark the following on the given shape.

BA �#� DC �#�

AEAB # BECE # CDDB #

BmAm � � BA �#�

356

80120

35

�

�

�

EBABCE

CEDmAEBmAm

D

D

D

1.3 Conditionals, Converse, Counterexample, and more definitions. Conditional- A sentence with a condition and then a result. Usually in the form of : If 43 �x , then 1 x If it rained, then the street is wet. What do these statements all have in common? If an D90 �Am , then A� is a right angle. If a polygon is a square, then it is a rhombus 1. Write a conditional. Converse- The reverse statement. If 1 x , then 43 �x If the street is wet, then it rained. What did I do to the previous statements to create these? If A� is a right angle , then the D90 �Am If a polygon is a rhombus, then it is a square 2. Write the converse to your conditional. Biconditional- A statement where the conditional and the converse are true and written using "if and only if." Examples. If 43 �x , then 1 x , If 1 x , then 43 �x 43 �x if and only if 1 x If an D90 �Am , then A� is a right angle. If A� is a right angle , then the D90 �Am A� is a right angle if and only if the D90 �Am 3. Can you write a biconditional using your conditional and converse? If not true, then try writing one using another scenario.

F

A

C

E

B D

Counterexample- An example that makes something not true. It counteracts the statement. 4. Given the conditional: If it rained, then the street is wet. a) Write the converse. b) Give a counterexample to disprove the converse. 5. Given the conditional: If 3 x , then 92 x a) Write the converse. b) Give a counterexample to disprove the converse.

Name Definition Picture (give a measurement)

Right Angle An angle with a measure

of 90 deg.

Acute angle

An angle with a measure of less than 90 deg.

obtuse angles

An angle with a measure of more than 90 deg.

Midpoint of a segment

The point equidistant from both endpoints

Angle bisector

The line segement equidistand from the segments creating the angle

6. Mark each figure to indicate the given information. Use the congruent slashes and symbol for a right angle.

a) AB = CD, m�A �m�D b) Point F is the midpoint of sAC, �CDB is a right angle, and sAE is an angle bisector.

.

A D

B C

Defining line and angle relationships.

Name Definition Picture (give a measurement) Short Form

Parallel lines

Two or more lines that lie in the same plane and do not intersect

ml

Perpendicular lines

Two lines that lie in the same plane and intersect at a 90 degree angle.

pm A

Pair of complementary

angles

Two angle whose measures have a sum of 90 degrees.

Pair of supplementary

angles

Two angle whose measures have a sum of 180 degrees.

Pair of vertical angles

Two nonadjacent angles formed by two intersecting lines

Linear pair of angles

A pair of angles that form a line.

Draw and carefully label the following: 1. Two vertical angles �1 and �2 2. ARPE A

3. PE ET 4. Supplementary angles D and F with D35 �Dm

m

p

lm

1.4

Defining POLYGONS (many knees) Polygon-- A closed figure in a plane, formed by a finite set of non collinear line segments.

Sides Name Sides Name Sides Name 2 6 10 3 7 11 4 8 12 5 9 p

Name Definition Picture

Convex polygon

A polygon where no segments connecting any two vertices can be drawn outside the polygon.

Concave polygon

A polygon were at least one segment connecting two vertices can be drawn outside the polygon

Consecutive vertices Two vertices connected by a side.

Consecutive sides Two sides that share a vertice

Consecutive angles Two angles that share a side

Congruent polygons

Polygons where all corresponding sides have equal measures and all corresponding angles have equal measures.

Name Definition Picture

Draw and carefully label the following: Use a ruler and protractor. 1. Hexagon HEXGON with right �G and diagonal sEO 2. Equiangular quadrilateral QUAD. 3. Draw a Hexagon ABCDEF where FDA �#�#� .

Diagonal A segment connecting two nonconsecutive vertices

Equilateral Polygon A polygon where all sides are equal.

Equiangular polygon A polygon where all angles are equal.

Regular polygon A polygon where all sides are equal and all angles are equal

1.5 Triangles

Name Definition Picture

Draw and carefully label the following: 1. An obtuse scalene triangle 2. Triangle ABC with median AE. 3. Acute triangle DEF with altitude DA 4. Obtuse triangle MOP, 130 �Om , with altitude ME.

Right triangle A triangle with one right angle

Acute triangle

A triangle where all angles are acute.

Obtuse triangle A triangle with one obtuse angle

Scalene triangle

A triangle where no sides are equal

Isosceles triangle A triangle with at least two congruent sides

Equilateral triangle A triangle where all sides are congruent

Median of a triangle

A segment connecting the midpoint of a side to the opposite vertex

Altitude of a triangle

A perpendicular segment from the vertex to the opposite side or the line containing the opposite side.

QUADRILATERALS

TRAPEZOIDS

RHOMBUS RECTANGLE

SQUARE

PARALLELOGRAMS KITES

1.6 Quadrilaterals

Name Definition Picture

Trapezoid A Quadrilateral with exactly on pair of

parallel sides

Kite A Quadrilateral with exactly two pairs of distinct congruent consecutive sides

Parallelogram A Quadrilateral with two pair of parallel sides.

Rhombus An equilateral Quadrilateral

Rectangle An equiangular Quadrilateral

Square An equiangular and equilateral Quadrilateral

Use your geometric tools to draw and label each figure. These must be close to exact.

9. Isosceles right triangle ABC with right angle B 10. Trapezoid ZOID with sZO // sID, m�OZD = 75°, and m�ZOI = 45°

Exercises--Group work---Review. Answer the following questions. Match each statement from 1 to 8 with a letter from the box.

a. Decagon e. Acute i. Collinear m. AB b. Isosceles f. Octagon j. Coplanar n. AB c. Scalene g. Hexagon k. Protractor o. �� o�

BA

d. Obtuse h. Dodecagon l. �� o�AB

p. �� omAB

1. _______ The tool used to measure angles in degrees 2. _______ Three or more points on a line 3. _______ A triangle with all sides of unequal measure 4. _______ A triangle with at least two sides of equal measure 5. _______ A ray starting at point B and passing through point A 6. _______ A line segment with endpoints A and B 7. _______ An angle whose measure is greater than 90° 8. _______ A polygon with ten sides

Match each statement from 1 to 8 with a letter from the box.

a. Rhombus e. Angle bisector i. Parallel b. Rectangle f. Median j. Supplementary c. Trapezoid g. Altitude k. Complementary d. Parallelogram h. Perpendicular bisector

1. _______ Two angles whose measures add up to 180° 2. _______ Two lines in the same plane that do not intersect 3. _______ An equiangular parallelogram 4. _______ A quadrilateral with exactly one pair of parallel sides 5. _______ An equilateral quadrilateral 6. _______ A segment in a triangle connecting a vertex with the

midpoint of the opposite side 7. _______ A segment in a triangle from a vertex perpendicular to

the line containing the opposite side 8. _______ A segment in a triangle from a vertex to the opposite

side dividing the angle into two parts of equal measure 9. True or False. If false, then give a counterexample or reason why it is false. a) _____An angle bisector divides an angle into two congruent angles. b) _____If two lines intersect then they form a right angle. c) _____Every square is a rectangle. d)_____Every square is a rhombus. e)_____An obtuse triangle has exactly one angle greater than 90 degrees

1.7 Circles Circle- The set of points in a plane equidistant form a given point(the center of the circle). radius- A segment from the center of the circle to a point on the circle (the distance from the center to a point on the circle.) Congruent Circles- two circles with the same radius. Concentric circles - Two circles with the same center Arc of a circle- part of a circle Semicircle- An arc that is half the circle Minor Arc- less than half the circle Major Arc- more than half Chord- a segment connecting two points on the circle. Diameter- a cord containing the center of the circle. Secant line- a line that intersects two or more points of a circle or curve. Tangent line- a line that intersects one and only one point on the object. Inscribed angle- An angle created by two different cords sharing a point on the circle. Central angle- an angle with vertex at the center of the circle

1.8 Space Geometry Let's do some drawing. Cylinder Cone Pyramid Prism Sphere Hemisphere 1. Draw a rectangular solid 3 cm by 4 cm by 5 cm, resting on its smallest face.

1.9 If you can't picture it then DRAW A PICTURE. 1. David is 3 years older than Stephen and 2 years younger than Graham. If Neil is 4 years younger than

Graham, how much older than Neil is David? ____________ 2 The box on the right is wrapped with two strips of ribbon as shown. What length of ribbon was needed to

decorate the box? Break the box down into it's six sides.

3. At one point in a race, Homer was 25 feet behind Bart and 28 feet ahead of Marge. Marge was trailing Lisa by 40 feet. Who is winning the race and by how much? How much is Homer losing the race by?

Locus- a set of points/dots. Planes can be paper, cardboard, or any flat surface. 4. Line AB lies in a plane. Sketch the locus of points in that plane that are 3 cm from line AB. Sketch the locus of points in the space that are 3 cm from line AB. What shapes do the locus of points make for each sketch? 5. Point P lies in the plane. Sketch the locus of points in that plane that are 3 cm from the point P. What shape do the locus of points make?