advertisement

Geo I HW 1-19 Name _________________ Date _____________ 1. Solve the system: -2(2x + 3y = 25) 4x – 9y = -55 4x – 9y = -55 4x – 9(7) = -55 4x – 63 = -55 4x = 8 x=2 2. UZ bisects IUQ. QUZ = 5x + 3y + 1 QUI = 20x + 3y + 3 ZUI = 8x + 2y + 2 20x + 3y +3 -4x – 6y = -50 4x – 9y = -55 -15y = -105 y=7 a) b) c) d) draw & label a picture write 2 equations solve for x & y find mQUI Go to the end for the rest of this problem. (not enough room) I Z 5x + 3y +1 U Q 3. The sum of twice an angle and its complement is 50 less than the angle’s supplement. Find the measure of the angle’s complement. 2x + 90 – x = 180 – x – 50 x + 90 = -x + 130 2x = 40 x = 20 complement = 70˚ 4. Identify all pairs of: Alt int s 5 & 1, 6 & 4 7 8 5 Alt ext s 8 & 2, 7 & 3 6 4 1 3 2 SSI s 6 & 1, 5 & 4 SSE s 8 & 3, 7 & 2 Corresponding s 6 & 2, 8 & 4, 7 & 1, 5 & 3 Vertical s 6 & 8, 2 & 4, 7 & 5, 1 & 3 Linear pairs 6 & 5, 2 & 1, 6 & 7, 2 & 3, 8 & 5, 4 & 1, 8 & 7, 4&3 A 5. Given: B is the midpoint of AD. m n 4 5 8 6 1B 3 2 C D 7 Give the reason of each statement. a) m // n given b) 1 3 vertical angle thm d) AB BD def midpoint e) 1 7 // lines alt int angles are congruent h) 4 +5 = 180 g) 2 +3 = 180 def linear pair // lines SSE angles sup c) AB + BD = AD segment addition postulate f) 2 +3 = ABD angle addition postulate **i) m bisects AD def bisect 6. Every Saturday Mrs. McCaleb sleeps in late. a) Write the statement as a conditional (if/then) If it is Saturday, then Mrs. McCaleb will sleep in. b) Underline p and circle q c) Write the converse. Is it true or false? If false, why? If Mrs. McCaleb sleeps in, then it is Saturday. False, I could sleep in on Columbus Day (which is a Monday). d) Write the inverse. Is it true or false? If false, why? If it is not Saturday, then Mrs. McCaleb won’t sleep. False, same as converse e) Write the contrapositive. Is it true or false? If false, why? If Mrs. McCaleb does not sleep in, then it is not Saturday. 7. 2x – 5y = 25 -5y = -2x + 25 m = _ 2/5 m // = _2/5 b = -5 m = -5/2 8. ABC is acute, and QRS is obtuse. Find the restrictions on x and y. A B Q C 0 < 3x + 15 < 90 -15 < 3x < 75 -5 < x < 25 2. (continued from page 1) R 90 < 5y – 20 < 180 110 < 5y < 200 22 < x < 40 S Options for equations: 8x + 2y + 2 = 5x + 3y + 1 3x – y = -1 8x + 2y + 2 + 5x + 3y + 1 = 20x + 3y + 3 13x + 5y + 3 = 20x + 3y + 3 -7x + 2y = 0 2(8x + 2y + 2) = 20x + 3y + 3 16x + 4y + 4 = 20x + 3y + 3 -4x + y = -1 2(5x + 3y + 1) = 20x + 3y + 3 10x + 6y + 2 = 20x + 3y + 3 -10x + 3y = 1 You should have 2 of the 4 equations above. Doesn’t matter which 2! I am going to use the purple and the green. Substitution: -y = -3x – 1 y = 3x + 1 -7x + 2(3x + 1) = 0 -7x + 6x + 2 = 0 -x = -2 x=2 -7(2) + 2y = 0 -14 + 2y = 0 2y = 14 y=7 Elimination (eliminating the y’s) 2(3x – y = -1) 6x – 2y = -2 -7x + 2y = 0 -x = -2 x=2 -7(2) + 2y = 0 -14 + 2y = 0 2y = 14 y=7 Elimination (eliminating the x’s) 7(3x – y = -1) 3(-7x + 2y = 0) 21x – 7y = -7 -21x + 6y = 0 -y = -7 y=7 -7x + 2(7) = 0 -7x + 14 = 0 -7x = -14 x=2