1. 1. Pairs of Angles Objectives: The student will be able to (I can): Classify angles as acute, right, or obtuse Identify linear pairs vertical angles complementary angles supplementary angles and set up and solve equations.
2. 2. acute angle right angle obtuse angle Angle whose measure is greater than 0 and less than 90. Angle whose measure is exactly 90. Angle whose measure is greater than 90 and less than 180.
3. 3. congruent angles Angles that have the same measure. mWIN = mLHS WIN LHS Notation: Arc marks indicate congruent angles. Notation: To write the measure of an angle, put a lowercase m in front of the angle bracket. mWIN is read measure of angle WIN L H S W IN
4. 4. interior of an angle Angle Addition Postulate The set of all points between the sides of an angle If D is in the interiorinteriorinteriorinterior of ABC, then mABD + mDBC = mABC (part + part = whole) Example: If mABD=50 and mABC=110, then mDBC=60 A B D C
5. 5. Example The mPAH = 125. Solve for x. P A T H (3x+7) (2x+8)
6. 6. Example The mPAH = 125. Solve for x. mPAT + mTAH = mPAH P A T H (3x+7) (2x+8)
7. 7. Example The mPAH = 125. Solve for x. mPAT + mTAH = mPAH 2x + 8 + 3x + 7 = 125 P A T H (3x+7) (2x+8)
8. 8. Example The mPAH = 125. Solve for x. mPAT + mTAH = mPAH 2x + 8 + 3x + 7 = 125 5x + 15 = 125 P A T H (3x+7) (2x+8)
9. 9. Example The mPAH = 125. Solve for x. mPAT + mTAH = mPAH 2x + 8 + 3x + 7 = 125 5x + 15 = 125 5x = 110 P A T H (3x+7) (2x+8)
10. 10. Example The mPAH = 125. Solve for x. mPAT + mTAH = mPAH 2x + 8 + 3x + 7 = 125 5x + 15 = 125 5x = 110 x = 22 P A T H (3x+7) (2x+8)
11. 11. angle bisector A ray that divides an angle into two congruent angles. Example: UY bisects SUN; thus SUY YUN or mSUY = mYUN S U N Y
12. 12. adjacent angles linear pair Two angles in the same plane with a common vertex and a common side, but no common interior points. Example: 1 and 2 are adjacent angles. Two adjacent angles whose noncommon sides are opposite rays. (They form a line.) Example: 1 2
13. 13. vertical angles Two nonadjacent angles formed by two intersecting lines. They are alwaysThey are alwaysThey are alwaysThey are always congruent.congruent.congruent.congruent. Example: 1 and 4 are vertical angles 2 and 3 are vertical angles 1 2 3 4
14. 14. complementary angles supplementary angles Two angles whose measures have the sum of 90. Two angles whose measures have the sum of 180. A and B are complementary. (55+35) A and C are supplementary. (55+125) A 55 B 35 C 125
15. 15. Practice 1. What is m1? 2. What is m2? 3. What is m3? 1 60 51 2 105 3
16. 16. Practice 1. What is m1? 180 60 = 120 2. What is m2? 3. What is m3? 1 60 51 2 105 3
17. 17. Practice 1. What is m1? 180 60 = 120 2. What is m2? 90 51 = 39 3. What is m3? 1 60 51 2 105 3
18. 18. Practice 1. What is m1? 180 60 = 120 2. What is m2? 90 51 = 39 3. What is m3? 105 1 60 51 2 105 3