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.