Definitions
Write the next statement (segments)
Name the reason.
Write the next statement (angles)
Solve for x
100
What is an adjacent pair of supplementary angles (add up to 180 degrees)?
Linear Pair of Angles
100
X is between D and F
DX + XF = DF
100
1. B is the midpoint of segment AC 1. Given
2. AB is congruent to BC 2. ???
Definition of Midpoint
100
Angle 1 and angle 3 are supplementary.
m angle 1 + m angle 3 = 180 degrees
100
Angle A and angle B form a linear pair.
m<A=(x+2)o
m<B=153o
x=25
200
A pair of opposite angles made by two intersecting lines that are congruent.
Vertical Angles
200
M is the midpoint of PQ.
PM is congruent to MQ
200
1. Angle 1 and Angle 2 are complementary 1. Given
2. m<1 + m<2 = 90 2. ???
Definition of complementary
200
<A is a right angle
m<A = 90
200
Angle C and angle D are complementary.
m<C=(4x+7)o
m<D=55o
x=7
300
Given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC. What postulate is this?
Segment Addition Postulate
300
AB = DF
BC = DF
AB = DF
300
1. BC is congruent to DE 1. Given
2. BC = DE 2. ??
Definition of Congruence
300
m<1 = 85o and m<2 = 85o
m<1 = m<2
300
Angle E and angle F are vertical angles.
m<E=(9x+2)o
m<F=65o
x=7
400
The point that divides a segment into two congruent segments.
Midpoint
400
In segment BC, BD is congruent to DC
D is the midpoint of BC
400
1. Angle 1 and angle 2 are supplementary. 1.Given
2. m<1+m<2=180 2. ???
Definition of Supplementary
400
<ABX ≅ <XBC
400
Point S is the midpoint of RT.
RS=8x-2
ST=3x-17
x=-3
500
Two angles that have a common side, common vertex, and don't overlap.
Adjacent Angles
500
BC is congruent to DE
BC = DE
500
1. Point E lies on segment DF. 1. Given
2. DE+EF=DF 2. ???
Segment Addition Postulate
500
<4 and <5 are vertical angles
m<4 = m<5
500
Points A, B, and C are collinear with B between A and C.
AC=3x+3
AB=-1+2x
BC=16
x=12