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Geometry Name: Date: Per.: 6.5 TRAPEZOIDS AND KITES Using the list of websites provided (or your own), complete the notes below. 1) Properties of Trapezoids: http://www,coolmath.com/reference/trapezoids.html#the_isosceles_trapezoid 2) Isosceles Trapezoid: http://www.mathwarehouse.com/geometry/quadrilaterals/isosceles-trapezoid,php 3) Trapezoid: http://w~w.mathopenref,com/trapezoid.html 4) Median of a Trapezoid: http://www,mathopenref.com/trapezoidmedian.html 5) Kite: http://www.mathopenref.com/kite,html 6) Properties of Kites: http://www,cootmath.com/reference/kites,html 7) Textbook Website (link from SchooIWires) TRAPEZOIDS Define the following terms and label the ports of each figure shown. 1) Trapezoid 2) Bases of a trapezoid 3) Base angles of a trapezoid 4) Legs of trapezoid 5) Isosceles trapezoid 6) Midsegment of a trapezoid MD/2-09/Notes 6.5 Trapezoids and Kites 1 Geometry THEOREMS RELATED TO TRAPEZOIDS. Fill in the missing information using the diagram and your research. THEOREM 6.1~T If a trapezoid is isoscetes, then each pair of base angles is THEOREM 6.15 If a trapezoid has a pair of congruent , then it is an isosceles t~apezoid, ABCD is an isosceles trapezoid, THEOREM 6.10 A trapezoid is isosceles if and only if its d~agonals are ABCD is isosceles if and only A D B C THEOREM 6,17: ~/IIDSE,GMENT THEOREM FOR TRAPEZOIDS The midsegment of a trapezoid is parallel B C to each base and its le~th is one half the M sum of the lengths of the bases, PRACTICE i. Find the angle measures of ABCD. A) MD/2-O9/Notes 6.5 Trapezoids and Kites 2 Geometry Find the measure of the midsegment RT. C) w KITES Define Kite List the properties of a kite and mark the diagram to reflect those properties. THEOREMS RELATED TO KITES. Fill in the missing information using the diagram and your research. C If a quadrilateral is a kite, then its diagonals ate B ~,,~.,~D A THEOREM 6.19 C If a quadrilateral is a kite, then exactly one pair of opposite angles ate congruent, ZA__ ZC, ZB __ ZD MD/2-O9/Notes 6.5 Trapezoids and Kites 3 Geometry PRACTICE Find the length of the sides to the nearest hundredth or the measure of the angles in kite KITE. K c) E ~,2o T STANDARDIZED TEST PRACTICE QUESTIONS 1) MMtIpI¢ Choiv~ h~ the [sosceies trapezoid ABCD, find 2)MMtiple Choice Find the [engt:la of~ in {he l:rape~oid beIow ~_ ,iB) 4 g ~+ 1 N 3)Multiple Choice The- mtdsegment of a trapezoid is 9 cm long. What choice bek)w is not a possible choice for the lengths of ~he bases? (~ 2, 1~5 @, 5 4 .~b 8 10 L M 4) M#itipie Choice ABCD is a ~,rapez.oi& Find the length of mic[segmen~ A 13 11 22 Mb/2-O9/Notes 6,5 Trapezoids and Kites B 4 NAME D~E Practice A For use with pages 356-363 Match the pair of segments or angles with the term, which describes them in trapezoid PQRS, 1. QR and PS A. bases B. legs 2. PQ and RS R C. diagonals D. base angles 3. QS and PR 4. /__Q and/-S 5. AS and !-P E, opposite angles P S Complete the statement with always, sometimes or never. 6, A trapezoid is ~? a parallelogram. 7. The bases of a trapezoid are ? paralle!. 8. The base angles of an isosceles trapezoid are ~? congruent. 9. The legs of a trapezoid are ? congruent. Find the angle measures of ABCD. 11. A 91° ) 12. 132o,~x //108° D,----..~--~ C D ~ o/ ) --C ~ Find the length of the midsegment ~-T. 15. W 22, Z !3 ) 12 Z y Y Find the length of the sides to the nearest hundredth or the measure of the angles in kite KITE. 16. / 17, K 18. K~ TE E~I T Copyright @ McDougal Littelt Inc. All rights reserved. 18 Geometry Chapter 6 Resource Book c DATE NAME -- Practice B For use with pages 356=363 Draw a trapezoid JKLM with JK II LM. Match the pair of segments or angles with the term, which describes them in trapezoid JKLM. 1. JK and ML 2. MJ and KL 4, /-K and/_M 5. JL and KM A. bases angles D. diagonals B. consecutive sides 3. ML and KL 6. Z_M and/-L C. opposite angles F. legs E. bases Find the angle measures of ABCD. The midsegment of the trapezoid is RT. Find the value of x. 10, 11, 7 12, 8 24 x 14 x Find the length of the sides to the nearest hundredth or the measure of the angles in kite MATH. 13. 14, A A 15, M H H T Write a two-column or a paragraph proof. 17 Given: ~ is a midsegment of ~XYZ. XZ-~ YZ 16. Given: DEIIAV, ADAV ~ AEVA Prove: DAVE is an isosceles trapezoid. Prove: XWVY is an isosceles trapezoid. D x ,E z Geometry Chapter 6 Resource Book Copyright@ McDougal Lit[ell Inc. Al! rights reserved, DATE NAME Practice C For use with pages 356-363 Decide whether the figure is a trapezoid. If it is, is it an isosceles trapezoid? 2, 1. Quadrilateral ABCD is a trapezoid with midsegment EF. Use the given information to answer the following. 4. Ifm/-B= 73°, thenm/-C= ? . A 5. If mZ_A = 51°andm!-C= 105°,then m/_D = ? 6. Ifm/-A = 48° and m/_C = 112°, then mZ_CFE =? . 7. IfAB=28andDC= 13, thenEF= ? . 8, IfEF= 13 and DC = 6, then AB = ? . 9. IfEF=x+ 5andDC+AB=4x+ 6, thenEF= ? Find the length of the sides to the nearest hundredth, or the measure of the angles in kite WEST. 10. 11. W 12, E w W~S E~’ T T S 13. In an isosceles trapezoid, if one pair of base angles is twice the measure of the second pair of base angles, what are the measures of the angles? 14. If the midsegment of a trapezoid measures 6 units long, what is tree about the S lengths of the bases of the trapezoid? Write a two-column or a paragraph proof. 15. Given: LORIis a rectangle. LB ~ DO AABC ~ ,~CDA Prove: BIRD is an isosceles trapezoid. L B D Copyright © McO0ugaI Littell Inc. All rights reserved. 16. Given: AF~:BC 0 Prove: ABCF is a trapezoid. O CF Geometry Chapter 6 Resource Book Geometry NAME: WORKSHEET:OtherQttadrilaterals.. PERIOD: DATE: Trapezoids and Kites Trapezoids A trapezoid is a with exactly one pair of be a parallelogram. By definition, a trapezoid can (always, sometimes, never) The sides that are parallel are called the The sides that are not parallel are called the A trapezoid is isosceles if Use the trapezoid to complete... a) the bases are A b) the legs are c) one pair of base angles: d) the other pair of base angles: e) Since RA//TP, mZT+ mZR = f) If TRAP is isosceles, then.., _= and mZ rnL =- mZ _~ mL Is it possible for the diagonals of a trapezoid to be congruent? Explain. The midsegment of a trapezoid is a segment that connects the midpoints of its legs. The midsegment has two interesting properties... I O/ I* 1) it is parallel to each base 2) its length is the average of the lengths of the bases. Complete the following. Z ~ a) Sketch in the midsegment of ZOID and include congruency marks. b) Find the length of the midsegment ifOI= 8 and ZD = 14. c) Write a general equation for finding the length of the midsegment of any trapezoid ZOID. Kites A kite is a with two pairs of congruentsides, but opposite sides are NOT By definition, a kite can (always, sometimes, never) be a parallelogram. Use the kite shown to answer the following. Do ANY angles appear congruent? Which? i Do diagonals appear congruent? Are the diagonals bisected? Do the diagonals appear perpendicular? Does a diagonal appear to bisect an angle? Properties of KITES 1) The diagonals of a kite are 2) Only one pair of opposite angles is 3) Only one diagonal is by the other diagonal. 4) Only one diagonal a pair of opposite angles. 5) Since a kite is a quadrilateral, the sum of the measures of its interior angles is Sketch a kite by using the properties of its diagonals. Find the perimeter of the kite below. Find the perimeter of the isosceles trapezoid. Geometry NAME: REVIEW: Trapezoids, Kites and Other Quads PERIOD: DATE: 1) Given: CH =- US. From just this information, which of the following are possible classifications of quadrilateral CUSH? (circle all that apply) C ~U H S Rectangle (non-square) ... Rhombus (non-square) ... Square ... Trapezoid (not isosceles) ... Isosceles Trapezoid ... Kite Indicate whether each statement is always, sometimes, or never true. 2) A trapezoid has two adjacent sides that are congruent. supplementary. 3) Consecutive angles in a kite are 4) Diagonals of a kite have opposite reciprocal slopes. 5) Given: NEMO is an isosceles trapezoid where NE//OM. E Ifm/_l = 100°,thenmZ2 = 6) What is the length of the midsegment of trapezoid MRLN? Show work. M 16.5 12.3 7) Use the figure to find the length of NL. L 6 9 NL= L 8) What is a possible length of each base of a trapezoid whose midsegment is 8.5cm long? Base 1 = Base 2 = Complete the following using the diagram of BRCE that is given. 9) IfmZ.1 = 35° and m/_5 = 55°, then m/-BRC = R U 10) IfBU= 15 and RE = 16, then BR = E Geometry NAME: WORKSHEET: Trapezoids in the Plane PERIOD: DATE: Trapezoids in the Coordinate Plane If you are given the vertices of a quadrilateral, you may determine whether it is a trapezoid it by characterizing its sides and/or diagonals. You start by calculating the slope of each side. If exactly one pair of opposite sides has the same slope, it’s a trapezoid. If the other sides are congruent (or the diagonals are congruent), then it is an isosceles trapezoid. Classify quadrilateral MARY with vertices M( -1, 2), A( 4, -3), R( 2, -7), Y( -5, 0) Geol~eti~y HOMEWORK: Trapezoids in the Plane NAME: Determine whether these quadrilaterals are trapezoids or isosceles trapezoids by: Calculating the slopes of the sides a) Calculating the lengths of diagonals or the lengths of the sides b) c) Classifying the quadrilateral as a trapezoid, isosceles trapezoid, or neither 1) Classify quadrilateral BERT, where B( -3, 5), E( 5, 4), R( 2, M), T(-4, -1) 2) Classify quadrilateral GVNR, where G( -6, -1), V(-2, 3), N( 5, -2), R(-1, -8)