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Fall 2012Geometry Exam Review
Chapter 1-5 Review p.200-201
Problems Answers1 One2 a. Yes, skew
b. No3 If you enjoy winter weather, then
you are a member of the skiing club.
4 -15 Transitive Property6 1807 1808 59 <110 Segment EB11 Bisects, 12 a. A and B
b. Ray SR and ray ST
Chapter 1-5 Review p.200-201
Problems Answers13
a. m<E14 17115 150, 15016 15, 15, 1617 3r - s18 Median19 Angle Bisector20 Isosceles21 72, 3622 Isosceles23 <ABC, <BAC, <ACD, and <CFD24 m>1=m>4=30; m<2=m<3=15
Chapter 1-5 Review p.200-201
Problems Answers25 m<1=m<4=k, m<2=m<3= 45-k26 Parallelogram27 <NOM, <LMO, <NMO28 Midpoint, segment MN29 PQ + ON
Chapter 1
Points, lines, planesCollinear, coplanar, intersectionSegments, rays, and distance (length)
Distance = |x2-x1|Congruent segments have ___________The segment midpoint divides the segment
__________A segment bisector intersects a segment at
_____
Chapter 1- Angles
Sides and vertexAcute, obtuse, right, straight (measure = ?)
Adjacent angles Have a common vertex and side but share no interior
pointsAngle bisector
Chapter 1 Postulates and Theorems
Segment Addition Postulate- If B is between A and C, then AB + BC = AC
Angle Addition Postulate m<AOB +m<BOC = m<AOC If <AOC is a straight angle, and B is not on line AC,
then m<AOB +m<BOC = 180
Chapter 1
A line contains at least _____ point(s). two
A plane contains at least _______ point(s) not in one line. three
Space contains at least _____ points not all in one plane. four
Through any three non-collinear points there is exactly ________. one plane
Chapter 1- p. 23
If two planes intersect, their intersection is a _____ line
If two lines intersect, they intersect in _______ exactly one point
Through a line and a point not on the line, there is exactly one plane
If two lines intersect, then _______ contains the lines exactly one plane
Properties from Algebra p.37
Properties of Equality Addition, Subtraction, Multiplication, Division Substitution Reflexive
(a=a) Symmetric
(if a=b, then b=a) Transitive Distributive
Properties of Congruence Reflexive Symmetric Transitive
Chapter 2
Midpoint Theorem p.43Angle Bisector Theorem p.44Complementary and supplementary angles p. 61Vertical anglesDefinition of Perpendicular lines p.56
Two lines that intersect to form right anglesIf two lines are perpendicular they form _______
Congruent adjacent anglesIf two lines form congruent adjacent angles, then
the two lines are______________ Perpendicular
Chapter 2
If the exterior sides of two adjacent acute angles are perpendicular, then the angles are ______ complementary
If two angles are supplements (complements) of congruent angles (or of the same angle), then the two angles are _____________ congruent
Chapter 3- Parallel Lines and Planes
Parallel lines Coplanar lines that do not intersect
Skew lines Non-coplanar lines that do not intersect and are not
parallelParallel planes
Planes that do not intersectIf two parallel planes are cut by a third plane,
the lines of intersection are ________ Parallel (think of the ceiling and floor and a wall)
Chapter 3
TransversalAlternate interior anglesSame-side interior anglesCorresponding angles
If 2 parallel lines are cut by a transversal, which sets of angles are congruent? Which are supplementary?
If a transversal is perpendicular to one of two parallel lines, it is __________ Perpendicular to the other one also
Ways to prove two lines are parallel Show a pair of corresponding angles are congruent Show a pair of alternate interior angles are congruent Show a pair of same-side interior angles are
supplementary In a plane, show both lines are perpendicular to a
third line Show both lines are parallel to a third line
Chapter 3- Classification of Triangles
Scalene, isosceles, and equilateralAcute, obtuse, right, and equiangular
Sum of the measures of the angles in a triangle = ?
Corollaries on p.94
Chapter 3- Polygons
Polygon- “many angles”Sum of the interior angles of a convex polygon with n sides
= ? (n-2)180
Measure of each interior angle of a convex polygon with n sides = ? (n-2)180/n
Sum of the measures of the exterior angles of any convex polygon = ? 360
Measure of each exterior angle of a regular convex polygon= ? 360/n
Chapter 4
Congruent figures have the Same size and shape Corresponding sides and angles are congruent
Naming congruent trianglesCPCTCSAS, SSS, ASA, AASHL, HA, LL, LAIsosceles Triangle Theorem and its Converse
Chapter 4
Corollary:The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
Equilateral and equiangular trianglesAltitudes, medians, and perpendicular bisectorsIf a point lies on the perpendicular bisector of a
segment, then the point is equidistant from the endpoints of the segment.
If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.
Distance from a point to a line
Chapter 5- Definitions and Properties
Properties of ParallelogramsParallelograms
Rectangle Rhombus Square
Trapezoids Median= ½ (b1 + b2)
Isosceles Trapezoids Base angles are congruent
Triangles Segment joining the midpoints of 2 sides Segment through the midpoint of one side and parallel to another side
Chapter 5
The midpoint of the hypotenuse of a right triangle is equidistant from the 3 vertices.
If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle. Pairs of opposite angles of a are congruent Measure of 4 interior angles of a add up to 360. Therefore all angles are right angles.
If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. Pairs of opposite sides in a are congruent Therefore all sides must be congruent
Chapter 11-Area
Parallelograms A= b*h Rectangle
A = b*h Rhombus
A= ½ d1 * d2 Square
A = s2
Trapezoids ½ (b1 + b2)*h
Triangles A= ½ b*h
The area of a region is the sum of the areas of its non-overlapping parts.