1. Splash Screen

2. Five-Minute Check (over Lesson 1–4) Then/Now New Vocabulary
Key Concept: Special Angle Pairs
Example 1: Real-World Example: Identify Angle Pairs
Key Concept: Angle Pair Relationships
Example 2: Angle Measure
Key Concept: Perpendicular Lines
Example 3: Perpendicular Lines
Key Concept: Interpreting Diagrams
Example 4: Interpret Figures
Lesson Menu

3. A B C D Refer to the figure. Name the vertex of 3. A. A B. B C. C
D. D A B C D
5-Minute Check 1

4. A B C D Refer to the figure. Name a point in the interior of ACB.
A. G
B. D
C. B
D. A A B C D
5-Minute Check 2

5. A B C D Refer to the figure. Which ray is a side of BAC? A. DB B. AC
C. BD
D. BC A B C D
5-Minute Check 3

6. Refer to the figure. Name an angle with vertex B that appears to be acute.
A. ABG
B. ABC
C. ADB
D. BDC A B C D
5-Minute Check 4

7. Refer to the figure. If bisects ABC, mABD = 2x + 3, and mDBC = 3x – 13, find mABD.
5-Minute Check 5

8. A B C D OP bisects MON and mMOP = 40°. Find the measure of MON.
5-Minute Check 6

9. You measured and classified angles. (Lesson 1–4)
Identify and use special pairs of angles.
Identify perpendicular lines.
Then/Now

10. Concept

11. Sample Answers: PIQ and QIS, PIT and TIS, QIU and UIT
Identify Angle Pairs
A. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair.
A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
Sample Answers: PIQ and QIS, PIT and TIS, QIU and UIT
Example 1

12. Sample Answers: PIU and RIS, PIQ and TIS, QIR and TIU
Identify Angle Pairs
B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles.
Sample Answers: PIU and RIS, PIQ and TIS, QIR and TIU
Example 1

13. A B C D A. Name two adjacent angles whose sum is less than 90.
A. CAD and DAE
B. FAE and FAN
C. CAB and NAB
D. BAD and DAC A B C D
Example 1a

14. A B C D B. Name two acute vertical angles. A. BAN and EAD
B. BAD and BAN
C. BAC and CAE
D. FAN and DAC A B C D
Example 1b

15. Concept

16. Plan Draw two figures to represent the angles.
Angle Measure
ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.
Understand The problem relates the measures of two supplementary angles. You know that the sum of the measures of supplementary angles is 180.
Plan Draw two figures to represent the angles.
Example 2

17. Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side.
Angle Measure
Solve
6x – 6 = 180 Simplify.
6x = 186 Add 6 to each side.
x = 31 Divide each side by 6.
Example 2

18. Use the value of x to find each angle measure.
mA = x mB = 5x – 6
= = 5(31) – 6 or 149
Check Add the angle measures to verify that the angles are supplementary.
mA + mB = 180
= 180
180 = 180 
Answer: mA = 31, mB = 149
Example 2

19. ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.
A. 1°, 1°
B. 21°, 111°
C. 16°, 74°
D. 14°, 76° A B C D
Example 2

20. Concept

21. ALGEBRA Find x and y so that KO and HM are perpendicular.
Perpendicular Lines
ALGEBRA Find x and y so that KO and HM are perpendicular.
Example 3

22. 84 = 12x Subtract 6 from each side. 7 = x Divide each side by 12.
Perpendicular Lines
90 = (3x + 6) + 9x Substitution
90 = 12x + 6 Combine like terms.
84 = 12x Subtract 6 from each side.
7 = x Divide each side by 12.
Example 3

23. 84 = 3y Subtract 6 from each side. 28 = y Divide each side by 3.
Perpendicular Lines
To find y, use mMJO.
mMJO = 3y + 6 Given
90 = 3y + 6 Substitution
84 = 3y Subtract 6 from each side.
28 = y Divide each side by 3.
Answer: x = 7 and y = 28
Example 3

24. A. x = 5
B. x = 10
C. x = 15
D. x = 20 A B C D
Example 3

25. Concept

26. Interpret Figures
A. Determine whether the following statement can be justified from the figure below. Explain.
mVYT = 90
Example 4

27. TYW and TYU are supplementary.
Interpret Figures
B. Determine whether the following statement can be justified from the figure below. Explain.
TYW and TYU are supplementary.
Answer: Yes, they form a linear pair of angles.
Example 4

28. VYW and TYS are adjacent angles.
Interpret Figures
C. Determine whether the following statement can be justified from the figure below. Explain.
VYW and TYS are adjacent angles.
Answer: No, they do not share a common side.
Example 4