6.6 trapezoids and kites 2016 ink.notebook. January 29, Page 30 Page Kites and Trapezoids. Trapezoid Examples and Practice.
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1 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 Page 30 Page Kites and Trapezoids Page 31 Page 32 Trapezoid Examples and Practice Page 33 1
2 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes 6.6 Trapezoids and Kites fter this lesson, you should be able to successfully apply the properties of a trapezoid and a kite. Press the tabs to view details. Press the tabs to view details. Lesson Objectives Standards Lesson Notes G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G.CO.11 G.CO.12 Prove theorems about parallelograms. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Quadrilaterals 2
3 trapezoid is a quadrilateral with exactly pair of parallel sides. The parallel sides are called and the nonparallel sides are called. n trapezoid is a trapezoid whose are congruent. The diagonals of an isosceles trapezoid are congruent. Each pair of base angles are The or midsegment of a trapezoid is the segment that joins the midpoints of the legs. The median is parallel to the bases and its measure is the sum of the measures of the bases. 3
4 6.6 trapezoids and kites 2016 ink.notebook January 29, múl 1. múc CD is an isosceles trapezoid. is a median. M 1 D 3. = 30, CD = 42, MN = 2 N C 4
5 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 CD is an isosceles trapezoid. 4. = 18, MN = 25, CD = is a median. M 1 2 N D C CD is an isosceles trapezoid. is a median. M 1 D 5. = 6x 3 MN = 15 CD = 8x + 5. Find x,, and CD. 2 N C 5
6 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 CD is an isosceles trapezoid. is a median. M 1 2 N D C CD is an isosceles trapezoid. is a median. M 1 D 6. mú1 = 4x 60 múc = 30 x. Find x, mú1, and múc. 7. mú = 4x + 40, múd = 3x. Find x, mú, and múd. 2 N C 6
7 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 kite is a quadrilateral with exactly two pairs of sides. 12 Unlike a parallelogram, the opposite sides of a kite are not congruent or parallel. D E Note that a kite has a line of symmetry. The diagonal that is NOT bisected is the line of symmetry. In this example, is the line of symmetry. Properties of a Kite 1) Diagonals are perpendicular (C ¼ D) 34 C 2) Only ONE diagonal is bisected (E is the midpoint of D but not of C) 3) 2 sets of consecutive sides congruent ( D and C CD) 4) ngles at ends of NON-bisected diagonal are bisected (Û1 Û2 and Û3 Û4) 5) ngles at ends of bisected diagonals are congruent (ÛDC ÛC) Example 1: If WXYZ is a kite, find múz. The measures of ÚY and ÚW are not congruent, so ÚX ÚZ. W 80 Z X múx + múy + múz + múw = 60 Y múx = and múz = 7
8 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 Example 2: If CD is a kite, find C. 5 4 P 12 The diagonals of a kite are perpendicular. Use the Pythagorean Theorem to find the missing length. C P2 + PC2 = C2 5 D C = 8
9 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 H 8. Find mújrk R G 9. If RJ = 3 and RK = 10, find JK J 10. If múghj = 90 and múgkj = 110, find múhgk. K 11. If HJ = 7, find HG. 12. If HG = 7 and GR = 5, find HR. H G R J 13. If múghj = 52 and múgkj = 95, find múhgk. K 9
10 Quadrilaterals 1. 4 sided 2D polygon 2. sum of internal s = 360 Isosceles Trapezoid Legs are iagonals are mon base 's are Trapezoid 1. EXCTLY ONE pair of «sides mon base 's are supplementary Parallelogram 1. both pairs of opp sides are «2. both pairs of opp sides are 3. ONE pair of opp sides are OTH «and 4. both pairs of opp 's are 5. diagonals bisect each other 6. Consecutive 's are supplementary Rectangle 1. 4 right 's 2. Diagonals are Rhombus 1. all sides are 2. Diagonals bisect 's 3. Diagonals º bisectors 4. Diagonals form 4 rt Ës Kite 1. 2 disjoint pairs of consecutive all sides 2. Diagonals bisect opp 's 3. Diagonals are º 4. one set of opp 's are On the Worksheet Square 1. oth a rectangle and a rhombus 2. Diagonals form 4 isosceles rt Ës Note: Once a property is listed, it filters down to all other figures. i.e. Quadrilaterals interior 's = 360, so every 4-sided figure's interior 's = 360 For trapezoid FEDC, V and Y are midpoints of the legs. 1. If FE = 18 and VY = 28, find CD Given a trapezoid, find the value of x. 3. V W 4. C 21x x If m F = 140 and m E = 125, find m D. U X D 55 10
11 Find each measure. 1. m S 2. m D HOMEWORK 6.6 Practice WS on Trapezoids and Kites Find each measure. 3. m M 4. RH 5. m T Find each measure. 6. m Q 11
12 7. m Y Find each measure. 8. C For trapezoid HJKL, T and S are midpoints of the legs. 9. If HJ = 14 and LK = 42, find TS. 10. If LK = 19 and TS = 15, find HJ 11. If HJ = 7 and TS = 10, find LK 12. If KL = 17 and JH = 9, find ST nswers: OOK Work p : 1, 2, 6 11, 16 21, 24 27, 53 57,
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