Transcript 7-1
7-1 Angle Relationships Learn to classify angles and find their measures. 7-1 Angle Relationships Vocabulary angle adjacent angles right angle supplementary angles acute angle complementary angles obtuse angle straight angle vertical angles congruent angles 7-1 Angle Relationships 7-1 Angle Relationships Additional Example 1: Classifying Angles Use the diagram to name each figure. A. two acute angles TQP, RQS mTQP = 43°; mRQS = 47° B. two obtuse angles SQP, RQT mSQP= 133°; mRQT = 137° 7-1 Angle Relationships Additional Example 1: Classifying Angles Use the diagram to name each figure. C. a pair of complementary angles TQP, RQS mTQP + mRQS = 43° + 47° = 90 B. two pairs of supplementary angles TQP, TQR mTQP + mTQR = 43° + 137° = 180 SQP, SQR mSQP + mSQR = 133° + 47° = 180 7-1 Angle Relationships Check It Out: Example 1 Use the diagram to name each figure. A. two acute angles AEB, CED mAEB = 15°; mCED = 75° B. two obtuse angles AEC, BED mAEC= 105°; mBED = 165° 7-1 Angle Relationships Check It Out: Example 1 Use the diagram to name each figure. C. a pair of complementary angles AEB, CED mAEB + mCED= 15° + 75° = 90 D. a pair of supplementary angles CED, AEC mCED + mAEC = 75° + 105° = 180 7-1 Angle Relationships Additional Example 2A: Finding Angle Measures Use the diagram to find each angle measure. If m1 = 37°, find m2. m1 + m2 = 180° 1 and 2 are supplementary. 37° + m2= 180° Substitute 37 for m1. Subtract 37 from both sides. –37° –37° m2 = 143° 7-1 Angle Relationships Additional Example 2B: Finding Angle Measures Use the diagram to find each angle measure. Find m3 = 37°. m2 + m3 = 180° 2 and 3 are supplementary. 143° + m3 = 180° Substitute 143 for m2. Subtract 143 from both sides. –143° –143° m3 = 37° 7-1 Angle Relationships Check It Out: Example 2 Use the diagram to find each angle measure. If m1 = 42°, find m2. m1 + m2 = 180° 1 and 2 are supplementary. 42° + m2= 180° Substitute 42 for m1. Subtract 42 from both sides. –42° –42° m2 = 138° 7-1 Angle Relationships Adjacent angles have a common vertex and a common side, but no common interior points. Angles 1 and 2 in the diagram are adjacent angles. Congruent angles have the same measure. Vertical angles are the nonadjacent angles formed by two intersecting lines. Angles 2 and 4 are vertical angles. Vertical angles are congruent. 7-1 Angle Relationships Additional Example 3: Application A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 1: Find mCBD. ABF CBD mABF = mCBD mCBD = 26 Vertical angles are congruent. Congruent angles have the same measure. Substitute 26 for mCBD. 7-1 Angle Relationships Additional Example 3 Continued A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 2: Find mDBE. mCBD + mDEB = 90° The angles are complementary. 26 + mDEB = 90° Substitute 26 for mCBD. –26° –26° Subtract 26 from both sides. mDEB = 64° 7-1 Angle Relationships Check It Out: Example 3 A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 1: Find mCBD. ABF CBD mABF = mCBD mCBD = 19 19 Vertical angles are congruent. Congruent angles have the same measure. Substitute 19 for mCBD. 7-1 Angle Relationships Check It Out: Example 3 Continued A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 2: Find mDBE. 19 mCBD + mDEB = 90° The angles are complementary. 19 + mDEB = 90° Substitute 19 for mCBD. –19° –19° Subtract 19 from both sides. mDEB = 71° 7-1 Angle Relationships Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 7-1 Angle Relationships Lesson Quiz Use the diagram to name each figure or find each angle measure. 1. a right angle Possible answer: CGD 2. two acute angles Possible answer: 1, 2 3. pair of complementary angles Possible answer: 3, 4 4. If m1 = 47°, then find m 3. 47° 5. Find m4. 43° 7-1 Angle Relationships Lesson Quiz for Student Response Systems 1. If m1 = 42°, then find m 3. A. 3° B. 42° C. 48° D. 90° 7-1 Angle Relationships Lesson Quiz for Student Response Systems 2. Name a pair of complementary angles. A. CGD B. AGF C. AGB, BGC D. CGD, DGF 7-1 Angle Relationships Lesson Quiz for Student Response Systems 3. Find mCGD. A. 3° B. 42° C. 90° D. 180°