Geometry Midterm Study Guide
2013 - 2014
Unit 1
Section 1-2: Points, Lines, and Planes

Point: dot on the coordinate plane; indicates a location; has no size

Line: two points connected and go in both directions forever

Plane: flat surface that extends in all directions

Ray: part of a line that has one endpoint and extends forever in the other direction

Segment: part of a line with two endpoints

Collinear Points: points that lie in the same line

Coplanar Points: points that lie in the same plane

Two lines always intersect at a point.

Two planes always intersect at a line.
Section 1-3: Measuring Segments

Ruler Postulate: The distance between points A and B on a number line is AB  A  B
o Distance is always positive

Segment Addition Postulate: If three points A, B, and C are collinear and B is between A

and C, then AB + BC = AC
Section 1-7: Midpoint & Distance in the Coordinate Plane

The midpoint of a segment is the point that divides the segment into two congruent
parts.
o Tick marks indicate congruence. Therefore, this means the lengths are equal.
 KL  LM
 L is the midpoint

Midpoint and Distance Formulas
On a Number Line
On a Coordinate Plane
Points A and B
A ( x1, y1) and B ( x 2, y 2 )
Distance: A  B
Midpoint:


AB
2
(x 2  x1)2  (y 2  y1)2


x1  x 2 y1  y 2
,
)
Midpoint: (
2
2

Distance:

Unit 2
Sections 1-4 & 1-5: Measuring Angles & Exploring Angle Pairs
Angle Addition Postulate: If B is in the interior of AOC then

mAOB  mBOC  mAOC .

Bisect: to divide into two congruent parts
Segment Bisector: segment, ray, line, or plane that
intersects a segment at its midpoint
Angle Bisector: a ray that divides and angle into two congruent angles
Complementary Angles: two angles that add up to 90°
Supplementary Angles: two angles that add up to 180°
Vertical Angles: two nonadjacent angles whose sides are opposite rays
Example:
1& 3 are vertical angles
2 & 4 are vertical angles


Linear pair: two adjacent angles that form a straight line
Example:
1& 2 are linear pairs

Adjacent Angles: two angles with a common vertex and side but no common interior points
Example:
ABC &CBD are adjacent angles

Vertical Angles Theorem: Vertical angles are 

Section 1-8 Review: Classifying Polygons
Polygon: closed plane figure made up of line segments that intersect at adjacent vertices

Convex: no line containing a side goes through the interior of the polygon

Concave: has at least one diagonal with points outside the polygon
Classifying Polygons
# of sides
Name
3
4
5
6
7
8
9
10
11
12
n
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
11-gon
Dodecagon
n-gon
Equilateral: all sides are =
Equiangular: all angles are =
Regular: convex, equilateral, and equiangular
Section 1-8: Perimeter, Circumference, & Area
Perimeter: distance around a polygon (units)
Circumference: distance around a circle (units)
Area: amount of surface enclosed by a figure (units2)
Section 2-5: Reasoning in Algebra & Geometry
Section 3-1: Lines & Angles
Definition
Symbols
Parallel lines:

Coplanar lines

Do not intersect

Symbol: ||


AE || BF

AD || BC

“is parallel to”


Skew lines:

noncoplanar

not parallel

do not intersect

AB and CG are
skew.


Parallel planes:

planes that do not
intersect
plane ABCD || plane EFGH
Diagram
Section 3-2 Properties of Parallel Lines
Corresponding angles: in the same position in each cluster

corresponding angles are equal
1& 5
2 & 6

3 & 7
4 & 8

Alternate interior angles: opposite sides of the transversal and inside the parallel lines

alternate interior angles are equal
4 & 5

2 & 7

Alternate exterior angles: opposite sides of the transversal and not in between the parallel lines


alternate exterior angles are equal
3 & 6
1& 8

Same side interior angles: same side of the transversal and inside the parallel lines



same side interior angles are supplementary
2 & 5
4 & 7
Section 3-3 Proving Lines Parallel
IF…
1. Corresponding angles are congruent
If 1  5 , then r s


2. Alternate interior angles are congruent
If 4  5 , then r s


3. Alternate exterior angles are congruent
If 1  8 , then r s


4. Same-side interior angles are supplementary
If m3 m5 180 , then r s

…THEN the lines are parallel

Section 3-7: Equations of Lines on the Coordinate Plane
y 2  y1
x 2  x1

Slope formula: m 

Slopeintercept form: y  mx  b

o
m = slope
o
b = y-intercept
o
You always need to find m first, then b
o
When you are given two points: First find the slope, then use slope-intercept form

Rules for graphing in slope intercept form:
1. Write the equation in slope intercept form ( y  mx  b)
2. Plot the y-intercept on the y-axis
3. Write the slope as a fraction

up /down
4. Use the slope to move
right /left
5. Graph the line (Must plot at least two points)

Special Lines
Horizontal
Vertical
y=?
x=?
Slope = 0
Slope = undefined
Section 3-8: Slopes of Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

Slopes of parallel lines are equal

Slopes of perpendicular lines are opposite reciprocals of one another
Unit 3
Sections 4-2, 4-3, & 4-6 : SSS, SAS, ASA, AAS & HL
SIDE-SIDE-SIDE (SSS)
 If three sides of one triangle are congruent to three sides of a second triangle, then the
two triangles are congruent.
SIDE-ANGLE-SIDE (SAS)
 If two sides and the included angle of one triangle are congruent to two sides and the
included angle of a second triangle, then the two triangles are congruent.
ANGLE-SIDE-ANGLE CONGRUENCE (ASA)
 If two angles and the included side of one triangle are congruent to two angles and the
included side of another triangle, then the triangles are congruent.
ANGLE-ANGLE-SIDE CONGRUENCE (AAS)
 If two angles and a NON-included side of one triangle are congruent to the corresponding
two angles and NON-included side of a second triangle then the two triangles are
congruent.
HYPOTENUSE-LEG CONGRUENCE (HL)
 If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of
another right triangle, then the triangles are congruent.
o For example, in the diagram below ∆ABC  ∆DEF, by HL.

Four things you are allowed to mark on your own:
1. Reflexive side (a side shared by two triangles where they touch)
2. Vertical angles
3. A right angle on the other side of a line
4. If the lines are parallel, then angles may be equal
Section 4-5: Isosceles & Equilateral Triangles
Triangle Names
SIDES
ANGLES
Scalene – no sides equal
Acute – all angles are acute (less than 90°)
Isosceles – at least two sides equal
Right – one angle equal to 90°
Equilateral – all sides equal
Obtuse – one angle is obtuse (greater than
90°)
Equiangular – all angles are equal
Isosceles Triangle Theorem: if two sides of a triangle are congruent, then the base angles are
congruent
Section 5-1: Midsegments of a Triangle

A midsegment of a triangle is a segment connecting the midpoints of two sides of the
triangle.