Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Perceived visual angle wikipedia , lookup
9-1 Angle Relationships Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 9-1 Angle Relationships Warm Up Solve. 1. x + 30 = 90 x = 60 2. 103 + x = 180 x = 77 3. 32 + x = 180 x = 148 4. 90 = 61 + x x = 29 5. x + 20 = 90 x = 70 9-1 Angle Relationships Problem of the Day Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, 1 of the class wants sausage on the 3 pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza? 1 6 9-1 Angle Relationships Sunshine State Standards MA.8.G.2.2 Classify and determine the measure of angles,… 9-1 Angle Relationships Vocabulary angle adjacent angles right angle supplementary angles acute angle complementary angles obtuse angle straight angle vertical angles congruent angles 9-1 Angle Relationships An angle () is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex. 9-1 Angle Relationships 9-1 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° 9-1 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 9-1 Angle Relationships Check It Out: Example 1 Use the diagram to name each figure. A. two acute angles AEB measures 58° and DEC measures 58° B. two obtuse angles AEC measures 148° and DEB measures 122° 9-1 Angle Relationships Check It Out: Example 1 Use the diagram to name each figure. C. a pair of complementary angles AEB measures 58° and DEC measures 32°. 58 + 32 = 90° D. a pair of supplementary angles AEC measures 148° and DEC measures 32°. 148 + 32 = 180°; AEB measures 58° and DEB measures 122°, 58 + 122 = 180° 9-1 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° 9-1 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° 9-1 Angle Relationships Check It Out: Example 2A Use the diagram to find each angle measure. If m3 = 142°, find m4. m3 + m4 = 180° 142° + m4= 180° –142° –142° m4 = 38° 9-1 Angle Relationships Check It Out: Example 2B Use the diagram to find each angle measure. Find m1. m1 + m4 = 180° m1 + 38° = 180° –38° m1 –38° = 142° 9-1 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. 9-1 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. 9-1 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° 9-1 Angle Relationships Check It Out: Example 3 Based on the map, what is the measure of BGC? AGB is congruent to EGF. mAGB = 42° mBGC + mAGB = 90° mBGC + 42° = 90° mBGC = 48° 9-1 Angle Relationships Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 9-1 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° 9-1 Angle Relationships Lesson Quiz for Student Response Systems 1. If m1 = 42°, then find m 3. A. 3° B. 42° C. 48° D. 90° 9-1 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 9-1 Angle Relationships Lesson Quiz for Student Response Systems 3. Find mCGD. A. 3° B. 42° C. 90° D. 180°