1. Exploring Angle Pairs
Skill 05

2. Objective
HSG-CO.1: Students are responsible for being able to identify special angle pairs and use their relationships to find angle measures.

3. Definitions
Angles that are two coplanar angles with a common side, common vertex, and no common interior points are called adjacent.
Two angles whose sides are opposite rays are called, vertical angles.
Two angles whose measures have a sum of 90ᵒ are complements to each other.

4. Definitions
Two angles whose measures have a sum of 180ᵒ are supplements to each other.
A pair of adjacent angles whose noncommon sides are opposite rays form a linear pair.
An angle bisector is a ray that divides an angle into two congruent angles.

5. Postulate 8 The Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.

6. Example 1; Identifying Angle Pairs
a) Are ∠𝐵𝐹𝐷 and ∠𝐶𝐹𝐷 adjacent angles? Explain.
No!
They have a common side and vertex, but they also have common interior points, so they are not adjacent.
b) Are ∠𝐴𝐹𝐵 and ∠𝐸𝐹𝐷 vertical angles? Explain.
No!
𝐹𝐴 and 𝐹𝐷 are opposite rays, but 𝐹𝐸 and 𝐹𝐵 are not, so the angles are not vertical.
c) Are ∠𝐴𝐹𝐸 and ∠𝐵𝐹𝐶 complementary? Explain. B A C F D E
62ᵒ
28ᵒ
118ᵒ
Yes!
𝑚∠𝐴𝐹𝐸+𝑚∠𝐵𝐹𝐶=62+28=90
So they are complementary.

7. Example 2; Making Conclusions from Diagrams
What can you conclude from the diagram?
∠1≅∠2
By the congruent angle markings.
∠3 and ∠5 are vertical
By definition of vertical angles
∠1 & ∠2/∠2 & ∠3/∠3 & ∠4/∠4 & ∠5/∠1 & ∠5 are adjacent. 1 2 3 4 5
By definition of adjacent angles
∠3 & ∠4 and ∠4 & ∠5 form a linear pair, so they are supplementary.
By Linear Pair Postulate

8. Example 3; Finding Missing Angles
∠𝐾𝑃𝐿 and ∠𝐽𝑃𝐿 are a linear pair, what are 𝑚∠𝐾𝑃𝐿 and 𝑚∠𝐽𝑃𝐿?
180= 2𝑥 𝑥+36
180=6𝑥+60 K P J L
𝟐𝒙+𝟐𝟒 °
𝟒𝒙+𝟑𝟔 °
120=6𝑥
𝒙=𝟐𝟎
𝑚∠𝐾𝑃𝐿=
𝒎∠𝑲𝑷𝑳=𝟔𝟒°
𝑚∠𝐽𝑃𝐿=
𝒎∠𝑱𝑷𝑳=𝟏𝟏𝟔°

9. #05: Exploring Angle Pairs
Questions?
Summarize Notes
Homework
Quiz