2. Find the measure of AC. 4. Find the measure of BD. 6. Find the measure of AB.

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1 7.3 Start Thinking xamine the diagram and determine if there appears to be enough information to conclude that the quadrilateral is a parallelogram. If there is not enough information, give an example of additional information that would allow you to prove the H 3. X Y W Z 7.3 Warm Up Use the points ( 2, 5 ), ( 5, 1 ), ( 3, 2 ), and ( 1, 2) find the indicated slope or measure. to 1. ind the slope of. 2. ind the measure of. 3. ind the slope of. 4. ind the measure of. 5. ind the slope of. 6. ind the measure of. 7.3 umulative Review Warm Up or the conditional statement, write the converse, the inverse, and the contrapositive. Then determine if each statement is true. 1. If a triangle is right, then it contains two acute angles. 2. If two lines have the same slope, then they are parallel. 3. If there is ice on the road, then I will not go shopping. opyright ig Ideas Learning, LL eometry Resources by hapter 241

2 Name ate 7.3 Practice In xercises 1 and 2, state which theorem you can use to show that the In xercises 3 and 4, find the value of x that makes the quadrilateral a parallelogram. 3. 3x x 3x + 2 5x x In xercises 5 and 6, graph the quadrilateral with the given vertices in a coordinate plane. Then show that the 5. ( 4, 2 ), ( 2, 1 ), ( 4, 1 ), ( 2, 2) 6. ( 4, 1 ), ( 1, 5 ), ( 11, 0 ), H( 8, 4) 7. Use the diagram to write a two-column proof. iven:, Prove: is a parallelogram. 8. In the diagram of the handrail for a staircase shown, m = 145 and. a. xplain how to show that is a parallelogram. b. escribe how to prove that is a parallelogram. c. an you prove that H is a parallelogram? xplain. H d. ind m, m, m, and m. 242 eometry opyright ig Ideas Learning, LL Resources by hapter

3 Name ate 7.3 Practice In xercises 1 and 2, state which theorem you can use to show that the In xercises 3 and 4, find the value of x that makes the quadrilateral a parallelogram x (2x + 5) 7x + 1 3x In xercises 5 and 6, graph the quadrilateral with the given vertices in a coordinate plane. Then show that the 5. W( 3, 1 ), X( 3, 4 ), Y( 3, 2 ), Z( 3, 3) 6. ( 4, 0 ), ( 2, 2 ), ( 5, 1 ), ( 1, 3) 7. Use the diagram to write a two-column proof. iven: is the midpoint of. is the midpoint of. Prove: is a parallelogram. 8. quadrilateral has two pairs of congruent angles. an you determine whether the quadrilateral is a parallelogram? xplain your reasoning. 9. n octagon star is shown in the figure on the right. a. ind m, m, and m b. State which theorem you can use to show that the c. The length of is three times the length of. Write an expression for the perimeter of parallelogram in terms of the variable x. opyright ig Ideas Learning, LL eometry Resources by hapter 243

4 Name ate 7.3 nrichment and xtension Proving That a Quadrilateral Is a Parallelogram In xercises 1 8, decide whether you are given enough information to determine that the 1. The opposite sides are parallel. 2. The opposite sides are congruent. 3. Two pairs of consecutive sides 4. Two pairs of consecutive angles are congruent. are congruent. 5. The diagonals are congruent. 6. The diagonals bisect each other. 7. ll four sides are congruent. 8. The consecutive angles are supplementary. 9. If two opposite angles of a quadrilateral measure 120 and the measures of the other angles are multiples of 10, what is the probability that the quadrilateral is a parallelogram? 10. The diagonals of quadrilateral H intersect at ( 1, 4 ). Two vertices of H are ( 2, 7 ) and ( 3, 5 ). What must be the coordinates of and H to ensure that H is a parallelogram? 11. In the diagram at the right, PQRS and QTSU are parallelograms. Is PTRU also a parallelogram? xplain why or why not. S P U T X Q R 12. onsider the supplementary angle relationships that you need to know to prove that a Make a conjecture using the least number of relationships that are necessary. 244 eometry opyright ig Ideas Learning, LL Resources by hapter

5 Name ate 7.3 Puzzle Time What Kind Of Ship an Last orever? ircle the letter of each correct answer in the boxes below. The circled letters will spell out the answer to the riddle. omplete the sentence. 1. If both pairs of opposite sides of a quadrilateral are, then the 2. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a. 3. If one of opposite sides of a quadrilateral are congruent and parallel, then the 4. If the diagonals of a quadrilateral each other, then the quadrilateral is a parallelogram. 5. quadrilateral is a parallelogram. Name the correct theorem number or give the correct value that would make the figure a parallelogram. 6. iven m = 72, find m. 7. iven m = m = 89, and m = m, indicate the theorem number that makes it a parallelogram. 8. O = 12, O = 12, O = 16. ind O. 9. = 4x + 2, = 5x 3, =. ind x. 10. = 2x + 1, = x + 8, =. ind x. O R O R N I M S always equal congruent side sometimes parallelogram I N S H I P supplementary 6 pair intersect bisect opyright ig Ideas Learning, LL eometry Resources by hapter 245