age 1 of 5 6.5 rapezoids Goal Use properties of trapezoids. trapezoid is a quadrilateral with eactly one pair of parallel sides. he parallel sides are the bases. he nonparallel sides are the legs. leg base leg Key Words trapezoid bases, legs, and base angles of a trapezoid isosceles trapezoid idsegent of a trapezoid trapezoid has two pairs of base angles. In trapezoid, a and a are one pair of base angles. a and a are the other pair. If the legs of a trapezoid are congruent, then the trapezoid is an. isosceles trapezoid base isosceles trapezoid HEOE 6.1 and 6.1 heore 6.1 Words If a trapezoid is isosceles, then each pair of base angles are congruent. ybols In the isosceles trapezoid, aca and aca. heore 6.1 Words If a trapezoid has a pair of congruent base angles, then it is isosceles. ybols In trapezoid, if aca then is isosceles. Visualize It! 10 10 Q In Eaple 1, fill in the issing angle easures as you find the. EXLE Q is an isosceles trapezoid. Find the issing angle easures. olution 1 Find ngle easures of rapezoids 1 Q is an isosceles trapezoid and a and a are a pair of base angles. o, a a. ecause a and a are sae-side interior angles fored by parallel lines, they are suppleentary. o, a 180 10. ecause aq and a are a pair of base angles of an isosceles trapezoid, aq a 10. hapter 6 Quadrilaterals
age of 5 Find ngle easures of rapezoids is an isosceles trapezoid. Find the issing angle easures. 1... 100 70 75 tudent Help VOULY I he idsegent of a trapezoid is soeties called the edian of a trapezoid. idsegents he idsegent of a trapezoid is the segent that connects the idpoints of its legs. he idsegent of a trapezoid is parallel to the bases. he length of the idsegent idsegent of a trapezoid is half the su of the lengths of the bases. 1 ( ) EXLE idsegent of a rapezoid Find the length of the idsegent G &** of trapezoid EFH. olution E 8 F G Use the forula for the idsegent of a trapezoid. 0 H G 1 (EF H) Forula for idsegent of a trapezoid 1 (8 0) ubstitute 8 for EF and 0 for H. 1 (8) 14 dd. ultiply. WE he length of the idsegent G &** is 14. idsegent of a rapezoid Find the length of the idsegent &** of the trapezoid. 4. 8 5. 6. 4 10 6 14 18 6.5 rapezoids
age of 5 6.5 Eercises Guided ractice Vocabulary heck 1. ae the bases of trapezoid.. ae the legs of trapezoid. kill heck ecide whether the quadrilateral is a trapezoid, an isosceles trapezoid, or neither.. 4. 5. Find the length of the idsegent. 6. 7 7. 8. 19 7 11 15 ractice and pplications Etra ractice ee p. 686. arts of a rapezoid atch the parts of trapezoid Q with the correct description. 9. Q &* and &* 10.aQ and a. legs. base angles 11. a and aq. opposite angles 1. &**. bases 1. Q&* and &* E. idsegent Hoework Help Eaple 1: Es. 14 19 Eaple : Es. 0 6 Finding ngle easures JKL is an isosceles trapezoid. Find the issing angle easures. 14. K L 15. K L 16. L 60 45 J K J J 18 4 hapter 6 Quadrilaterals
age 4 of 5 Finding ngle easure Q is a trapezoid. Find the issing angle easures. 17. 18. 19. 1 78 110 78 1 Finding idsegents Find the length of the idsegent &** of the trapezoid. 0. 9 1. 14. 15 9 7 16 Using lgebra Find the value of.. 4. 16 5. 9 10 7 ake esign 1 6. ake esign he top layer of the cake in the diagra at the right has a diaeter of 10 inches. he botto layer has a diaeter of inches. What is the diaeter of the iddle layer? 10 in. in. KE EIGE for and sculpt shapes and figures onto cakes by using tools such as icing bags, handade paper cones, or cutters. oordinate Geoetry he vertices of a trapezoid are (, 6), (8, 6), (8, ), and (4, ). 7. lot the vertices on a coordinate plane. onnect the to for trapezoid. 8. ae the bases of trapezoid. 9. ae the legs of trapezoid. 0. Find the coordinates of the idpoint of each leg. hen plot these points on the coordinate plane you drew in Eercise 7. What is the line segent that connects these two points called? 6.5 rapezoids 5
age 5 of 5 Itudent Help I L Z O E. O HOEWOK HEL Etra help with proble solving in Es. 1 is at classzone.co Visualize It! In Eercises 1, use the figures shown below. he figure on the left is a trapezoid with idsegent of length. he figure on the right is fored by cutting the trapezoid along its idsegent and rearranging the two pieces. 4 1 9 5 4 9 5 1 1. Which theore or postulate fro hapter can you use to show that a1 ca and a ca4 in the figure on the left?. What kind of quadrilateral is on the right? Eplain your answer.. hallenge How does the diagra help you see that the length of the idsegent is half the su of the lengths of the bases? tandardized est ractice 4. ultiple hoice In the trapezoid at the right, what is the value of? 1 15 J 1 15 17 8 K L 5. ultiple hoice Which of the following ust a trapezoid have? F congruent bases G diagonals that bisect each other H eactly one pair of parallel sides J a pair of congruent opposite angles ied eview Logical easoning ell whether the quadrilateral is a parallelogra. Eplain your reasoning. (Lesson 6.) 6. 7. 8. 115 65 lgebra kills ultiplying ultiply. Write the answer in siplest for. (kills eview, p. 659) 9. 1 0 40. 5 1 4 41. 16 1 8 4. 4 60 4. 7 44. 7 8 14 45. 5 6 1 46. 4 1 7 16 6 hapter 6 Quadrilaterals