1. Objectives
a. Identify adjacent, vertical, complementary, and supplementary angles.
b. Find measures of pairs of angles.
c. Find the co-ordinates of the midpoint of a line.
d. Find the distance between two points

2. Vocabulary adjacent angles linear pair complementary angles
supplementary angles
vertical angles
Mid Point Formula
Distance Formula
Pythagorean Theorem

4. Example 1A: Identifying Angle Pairs
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
AEB and BED
AEB and BED have
a common vertex, E,
a common side, EB,
no common interior points.
Their noncommon sides, EA and ED, are opposite rays.
AEB and BED are adjacent angles and form a linear pair.

5. Example 1B: Identifying Angle Pairs
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
AEB and BEC
AEB and BEC have a common vertex, E,
a common side, EB
no common interior points.
AEB and BEC are only adjacent angles.

6. Example 1C: Identifying Angle Pairs
Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.
DEC and AEB
DEC and AEB share E
do not have a common side
DEC and AEB are not adjacent angles.

8. You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°.
You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

9. Example 1: Finding the Measures of Complements and Supplements
Find the measure of each of the following.
A. complement of F
(90 – x)
90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)

10. Practice 1
mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary, find the measure of each angle.
2. If XYZ and PQR are complementary, find the measure of each angle.
40°; 140°
22°; 68°

11. m2 = 47°, m3 = 43°, and m4 =43°. Practice 2
Light passing through a fiber optic cable reflects off the walls of the cable in such a way that 1 ≅ 2, 1 and 3 are complementary, and 2 and 4 are complementary.
If m1 = 47°, find m2, m3, and m4.
m2 = 47°, m3 = 43°, and m4 =43°.

12. Another angle pair relationship exists between two angles whose sides form two pairs of opposite rays. Vertical angles are two nonadjacent angles formed by two intersecting lines. 1 and 3 are vertical angles, as are 2 and 4.

13. Name the pairs of vertical angles.
Practice 1
Name the pairs of vertical angles.
HML and JMK are vertical angles.
HMJ and LMK are vertical angles.
Check mHML  mJMK  60°.
mHMJ  mLMK  120°.

15. Example 1: Finding the Coordinates of a Midpoint
Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).
= (–5, 5)

16. Example 2: Finding the Coordinates of an Endpoint
M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:

17. Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates equal.
Multiply both sides by 2.
12 = 2 + x
Simplify.
2 = 7 + y
– 7 –7
– 2 –2
Subtract.
–5 = y
10 = x
Simplify.
The coordinates of Y are (10, –5).

18. Practice 1
S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T.
The coordinates of T are (4, 3).