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Geometry Unit 1: Lesson 1.4 Name: _______________________________ Date: _________________ Period: _______ Special Angles Essential Questions: o How do algebra and geometry work together within the coordinate plane? Goal: I can understand an algebraic relationship exists between: adjacent segments, adjacent angles, and special angle pairs. Key Ideas/Vocabulary: Diagram: Vertical Angles Complementary Angles Supplementary Angles Linear Pairs o Postulates/Theorems: Postulate 11 – Linear Pair Postulate If two angles form a linear pair, then they are supplementary, i.e., the sum of their measures is 1800. Theorem 2.1 – Congruent Supplements Theorem If two angles are supplementary to the same angle or to congruent angles, then they are congruent. Theorem 2.2 – Congruent Complements Theorem If two angles are complementary to the same angle or to congruent angles, then they are congruent. Theorem 2.3 – Vertical Angles Theorem If two angles are vertical angles, then they are congruent. Section 1: Identifying Special Pairs of Angles 1) Use the terms defined above to describe YT 1) Use the terms defined above to describe relationships between the labeled angles. relationships between the labeled angles. Answer: 2 1 5 4 3 Answer: Section 2: Angle Measures 2) Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the other angle. YT 2) Find the measures of two complementary angles if one angle measures eleven degrees more than seven times the measure of the other. Answer: Answer: 3) Find mSQT and mTQR . YT 3) Find mAEC and mCEB . Answer: mSQT = mTQR = 4) A supplement of an angle is six times as large as a complement of the angle. Find the measures of the angle, its supplement, and its complement. Answer: mAEC = Answer: 5) Find the measure of angles 1, 2, 3, 4, and 5. Angle 4 and 500 are complementary. Answer: YT 5) BD bisects ABC. Find mABD and find mABC. A mCEB = YT 4) Find x and y. B 5 Answer: x2 – 3x 44+4x xx+ 6 D C m1 _______, m2 _______, m3 _______, m4 _______, m5 _______ Answer: Section 3: Interpret Figures 6) Determine whether each statement can be assumed from the figure below. TRUE or FALSE. YT 6) Determine whether each statement can be assumed from the figure below. TRUE or FALSE. Answers: _____a.) mVYT 90 _____b.) TYW and TYU are supplementary. _____c.) VYW and TYS are adjacent angles. _____d.) TYW and VYS are linear pairs. Homework: mABD = Answers: _____a.) mXAY 90 _____b.) TAU and UAY are complementary. _____c.) UAX and UXA are adjacent angles. _____d.) ZAT and TAU are linear pairs. Special Angles – Supplement Worksheet # 6 Lesson Summary: mABC = Name______________________________________________Period__________Date____________________ SPECIAL ANGLES - SUPPLEMENT WORKSHEET # 6 Complementary and Supplementary Angles 1. If A and B are complementary and mA = 36, find mB 2. A and B are complementary, mA = 3x + 11 and mB = 2x + 19. Find… a. x = b. mA = c. mB = 3. If A and B are supplementary and mA = 56, find mB 4. If an angle is acute, what can you say about its supplement? 5. If mA = 4x + 31 and mB = 2x – 7, what is the measure of each angle if they are supplementary? For #’s 6 – 9 use the diagram above. 6. If m1 = 100, find m2 = ___ and m4 = . 7. If m2 = 56, find m1 = . and m3 = 8. If m3 = 145, find m2 = ___ and m4 = . 9. If m4 = 37, find m1 = . ___ and m3 = For #’s 10 – 14, use the diagram provided. 2 1 10. Name the complement of 1. _______________ 3 11. Name 2 angles complementary to 2. ______________ 12. If m2 = 36, find m1 = and m3 = 13. If m2 = 17, find m1 = and m3 = 14. What can you conclude about 1 and 3? ______________________________ Vertical Angles 15. m1 = 2x + 6, m3 = 3x -4 x= 1 4 2 m1 = 3 m2 = m3 = m4 = _____ 16. m2 = 5x – 10, m4 = 3x + 16 17. m1 = 3x +12, m2 = 2x + 3 x= x= m1 = m1 = m2 = m2 = m3 = m3 = m4 = m4 =