1. 1-5 : Angle Pair Relationships
Geometry Chapter 1
1-5 : Angle Pair Relationships

2. Warm-Up – Review Problems 5-8 From Quiz #1
Find the distance between the points.
5.) −6, 0 , (−6, 7)
𝑑= ( 𝑥 2 − 𝑥 1 ) 2 + ( 𝑦 2 − 𝑦 1 ) 2
𝑑= (−6−(−6)) 2 + (7−0) 2 𝑑=
𝒅= 𝟒𝟗 =𝟕
6.) 4, 5 , (−5, −8)
𝑑= ( 𝑥 2 − 𝑥 1 ) 2 + ( 𝑦 2 − 𝑦 1 ) 2
𝑑= (4−(−5)) 2 + (−8−5) 2
𝑑= (−13) 2 𝑑=
𝒅= 𝟐𝟓𝟎 ≈𝟏𝟓.𝟖𝟏

3. Warm-Up – Review Problems 5-8 From Quiz #1
Find the midpoint of the line segment with the given endpoints.
7.) −8, 5 , (3, 2)
𝑀= 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2
𝑀= −8+3 2 ,
𝑴= −𝟓 𝟐 , 𝟕 𝟐
8.) −3, −5 , (3, −5)
𝑀= 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2
𝑀= −3+3 2 , −5+(−5) 2
𝑀= 0 2 , −10 2
𝑴= 𝟎, −𝟓

4. Describe Angle Pair Relationships
Objective: Students will be able to use special angle relationships to find angle measures.
Agenda
Angle Types (w/Examples)
Angle Pairs (w/Examples)

5. Complementary and Supplementary Angles
Complementary Angles:
Two Angles whose measures add up to 90° 1
<𝟏 and <𝟐 are Complementary 2
𝒎<𝟏+𝒎<𝟐=𝟗𝟎°

6. Complementary and Supplementary Angles
Two Angles whose measures add up to 180°
<𝟑 and <𝟒 are Supplementary 3 4
𝒎<𝟑+𝒎<𝟒=𝟏𝟖𝟎°

7. Example 1 (Pg. 36) Solution: 𝑚<1+𝑚<2=90° 68 + 𝑚<2=90
a.) Given that <1 is a complement of <2 and 𝑚<1=68°, find 𝑚<2. b.) Given that <3 is a supplement of <4 and 𝑚<4=56°, find 𝑚<3.
Solution:
𝑚<1+𝑚<2=90°
68 + 𝑚<2=90
𝑚<2=22°
Solution:
𝑚<3+𝑚<4=180°
𝑚<3+56=180
𝑚<3=124°

8. Adjacent Angles Adjacent Angles:
Two Angles that share a common vertex and side, but have no common interior points.
Examples 5 6 7 8
<5 and <6 are complementary
<7 and <8 are Supplementary

9. Example 2 (Pg. 35) 32° 122° A C B D 58° R S T
In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles
32°
122° A C B D
58° R S T
Complementary Angles: <𝐵𝐴𝐶 and <𝑅𝑆𝑇
Supplementary Angles: <𝐷𝐴𝐶 and <𝑅𝑆𝑇
Adjacent Angles: <𝐵𝐴𝐶 and <𝐷𝐴𝐶

10. 𝑚<𝐵𝐶𝐸+𝑚<𝐸𝐶𝐷=180° (why?)
Example 3 (Pg. 36)
Find 𝑚<𝐵𝐶𝐸 and 𝑚<𝐸𝐶𝐷.
Solution:
𝑚<𝐵𝐶𝐸+𝑚<𝐸𝐶𝐷=180° (why?)
4𝑥+8 + 𝑥+2 =180
5𝑥+10=180
5𝑥=170
𝒙=𝟑𝟒
(4𝑥+8)°
(𝑥+2)° C E B D

11. Example 3 (Pg 36) Next, plug in 𝑥=34 for 𝒎<𝑩𝑪𝑬 and 𝒎<𝑬𝑪𝑫.
𝒎<𝑩𝑪𝑬=𝟒𝒙+𝟖
=𝟒 𝟑𝟒 +𝟖
=𝟏𝟒𝟒
For 𝒎<𝑬𝑪𝑫:
𝒎<𝑬𝑪𝑫=𝒙+𝟐
=𝟑𝟒+𝟐
=𝟑𝟔
Thus, 𝒎<𝑩𝑪𝑬=𝟏𝟒𝟒° and 𝒎<𝑬𝑪𝑫=𝟑𝟔°

12. Angle Pairs Linear Pair:
Two adjacent angles whose noncommon sides form opposite sides.
These angles are always supplementary. 1 2
<𝟏 and <𝟐 are a linear pair.
𝒎<𝟏+𝒎<𝟐=𝟏𝟖𝟎°

13. Angle Pairs Vertical Angles:
Two Angles whose sides form two pairs of opposite rays.
Angles that are directly across from one another on intersecting lines.
<𝟑 and <𝟔 are vertical angles. 5 6 4 3
<𝟒 and <𝟓 are vertical angles.

14. Example 4 (Pg. 37) Vertical Angles: <𝟏 and <𝟓 2 3 1 Linear Pair:
Identify all the linear pairs and all of the vertical angles in the figure.
Vertical Angles:
<𝟏 and <𝟓 5 2 4 3 1
Linear Pair:
<𝟏 and <𝟒
Also
<𝟒 and <𝟓

15. Example 5 (Pg. 37) 𝑚<1=𝑥° 𝑚<2=𝑚<1×5 𝑚<2=5𝑥° 5𝑥° 𝑥°
Two angles form a linear pair. The measure of one angle is 5 time the measure of the other. Find the measure of each.
Solution: First establish variables from information given in the problem
𝑚<1=𝑥°
𝑚<2=𝑚<1×5
𝑚<2=5𝑥°
Picture (If needed):
5𝑥° 𝑥°

16. Example 5 (Pg. 37) Thus, 𝒎<𝟏=𝟑𝟎° and 𝒎<𝟐=𝟏𝟓𝟎°
Solution: Now make an equation (using knowledge of linear pairs) and solve
Now plug in 𝑥=30 to find 𝑚<1 and 𝑚<2
𝑚<1+𝑚<2=180°
𝑥+5𝑥=180
6𝑥=180
𝑥=30
𝒎<𝟏=𝒙=𝟑𝟎
𝒎<𝟐=𝟓𝒙=𝟓 𝟑𝟎 =𝟏𝟓𝟎
Thus, 𝒎<𝟏=𝟑𝟎° and 𝒎<𝟐=𝟏𝟓𝟎°

17. Homework 1-5 Pg
#’s