Transcript Slide 1
9-3 Angle Relationships California Standards MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms. Holt CA Course 1 9-3 Angle Relationships Vocabulary vertical angles adjacent angles complementary angles supplementary angles 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. 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. 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 6 5 and 6 are opposite each other and are formed by two intersecting lines. They are vertical angles. 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 8 7 and 8 are side by side and have a common vertex and ray. They are adjacent angles. 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. 3 4 They are adjacent angles. Holt CA Course 1 9-3 Angle Relationships Check It Out! Example 1 Tell whether the numbered angles are adjacent or vertical. B. 7 8 7 and 8 are opposite each other and are formed by two intersecting lines. They are vertical angles. Holt CA Course 1 9-3 Angle Relationships Complementary angles are two angles whose measures have a sum of 90°. 65° + 25° = 90° LMN and NMP are complementary. L N 65° 25° M Holt CA Course 1 P 9-3 Angle Relationships Supplementary angles are two angles whose measures have a sum of 180°. 65° + 115° = 180° GFE and HJK are supplementary. E H 65° G Holt CA Course 1 115° F J K 9-3 Angle Relationships Additional Example 2: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. A. OMP and PMQ To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. P Q mOMP = 75° – 15° = 60°. Since 60° + 30° = 90°, PMQ and OMP are complementary. Holt CA Course 1 O N M R 9-3 Angle Relationships Reading Math 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°. Holt CA Course 1 9-3 Angle Relationships Additional Example 2: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. B. NMO and OMR mNMO = 15° and mOMR = 165° P Since 15° + 165° = 180°, NMO and OMR are supplementary. Q O N M Holt CA Course 1 R 9-3 Angle Relationships Additional Example 2: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. C. PMQ and QMR To find mPMQ, start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° – 75° = 30°. mQMR = 75°. P Q Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor supplementary. Holt CA Course 1 O N M R 9-3 Angle Relationships Check It Out! Example 2 Use the diagram to tell whether the angles are complementary, supplementary, or neither. A. BAC and CAF mBAC = 35° and mCAF = 145° Since 35° + 145° = 180°, BAC and CAF are supplementary. D E C F B A Holt CA Course 1 9-3 Angle Relationships Check It Out! Example 2 Use the diagram to tell whether the angles are complementary, supplementary, or neither. B. CAD and EAF To find mCAD, start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° – 35° = 55°. mEAF = 35°. D Since 55° + 35° = 90°, CAD and EAF are complementary. E C B F A Holt CA Course 1 9-3 Angle Relationships Check It Out! Example 2 Use the diagram to tell whether the angles are complementary, supplementary, or neither. C. BAC and EAF mBAC = 35° and mEAF = 35° Since 35° + 35° = 70°, BAC and EAF are neither supplementary C nor complementary. D E F B A Holt CA Course 1