1. Holt CA Course 1 9-3 Angle Relationships Warm Up Warm Up Lesson Presentation California Standards Preview

2. Holt CA Course 1 9-3 Angle Relationships Warm Up Classify each angle with the given measure as acute, right, obtuse, or straight. 1. 125°2. 90° 3. 85°4. 180° acute right obtuse straight

3. Holt CA Course 1 9-3 Angle Relationships MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms. California Standards

4. Holt CA Course 1 9-3 Angle Relationships Vocabulary vertical angles adjacent angles complementary angles supplementary angles

5. Holt CA Course 1 9-3 Angle Relationships Angles are congruent if they have the same measure. Adjacent angles are two angles that are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent. MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ and QRP are adjacent angles. They share vertex R and RQ.

6. Holt CA Course 1 9-3 Angle Relationships Vertical angles are two angles that are formed by two intersecting lines and are not adjacent. Vertical angles have the same measure, so they are always congruent. MRP and NRQ are vertical angles. MRN and PRQ are vertical angles.

7. Holt CA Course 1 9-3 Angle Relationships Additional Example 1: Identifying Adjacent and Vertical Angles Tell whether the numbered angles are adjacent or vertical. A. 5 and 6 are opposite each other and are formed by two intersecting lines. They are vertical angles. 5 6

8. Holt CA Course 1 9-3 Angle Relationships Additional Example 1: Identifying Adjacent and Vertical Angles Tell whether the numbered angles are adjacent or vertical. B. 7 and 8 are side by side and have a common vertex and ray. They are adjacent angles. 7878

9. Holt CA Course 1 9-3 Angle Relationships Check It Out! Example 1 Tell whether the numbered angles are adjacent or vertical. A. 3 and 4 are side by side and have a common vertex and ray. They are adjacent angles. 3 4

10. Holt CA Course 1 9-3 Angle Relationships Check It Out! Example 1 Tell whether the numbered angles are adjacent or vertical. B. 7 and 8 are opposite each other and are formed by two intersecting lines. They are vertical angles. 7 8

11. Holt CA Course 1 9-3 Angle Relationships 65° + 25° = 90° LMN and NMP are complementary. Complementary angles are two angles whose measures have a sum of 90°. P N M L 25° 65°

12. Holt CA Course 1 9-3 Angle Relationships Supplementary angles are two angles whose measures have a sum of 180°. 65° + 115° = 180° GFE and HJK are supplementary. K E F 115°65° G H J

13. Holt CA Course 1 9-3 Angle Relationships Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2: Identifying Complementary and Supplementary Angles A. OMP and PMQ Since 60° + 30° = 90°, PMQ and OMP are complementary. O N PQ R M To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. mOMP = 75° – 15° = 60°.

14. Holt CA Course 1 9-3 Angle Relationships If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle you are measuring is acute, its measure is less than 90°. Reading Math

15. Holt CA Course 1 9-3 Angle Relationships Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2: Identifying Complementary and Supplementary Angles B. NMO and OMR mNMO = 15° and mOMR = 165° O N P Q R M Since 15° + 165° = 180°, NMO and OMR are supplementary.

16. Holt CA Course 1 9-3 Angle Relationships Use the diagram to tell whether the angles are complementary, supplementary, or neither. Additional Example 2: Identifying Complementary and Supplementary Angles C. PMQ and QMR Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary. To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. mQMR = 75°. O N PQ R M

17. Holt CA Course 1 9-3 Angle Relationships Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out! Example 2 A. BAC and CAF mBAC = 35° and mCAF = 145° C B D E F A Since 35° + 145° = 180°, BAC and CAF are supplementary.

18. Holt CA Course 1 9-3 Angle Relationships Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out! Example 2 B. CAD and EAF Since 55° + 35° = 90°, CAD and EAF are complementary. C B D E F A To find mCAD, start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° – 35° = 55°. mEAF = 35°.

19. Holt CA Course 1 9-3 Angle Relationships Use the diagram to tell whether the angles are complementary, supplementary, or neither. Check It Out! Example 2 C. BAC and EAF mBAC = 35° and mEAF = 35° C B D E F A Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary.

20. Holt CA Course 1 9-3 Angle Relationships Lesson Quiz 1. Tell whether the numbered angles are vertical or adjacent. adjacent 6 7 Use the diagram to tell whether the angles are complementary, supplementary, or neither. 2. AZB and BZC 3. BZC and CZD neither complementary