# Section 7.5 Properties of Trapezoids and Kites 399 Using Properties of Isosceles Trapezoids The stone above the arch in the diagram is an isosceles trapezoid. Find m∠K, m∠M, and m∠J.

Given an isosceles trapezoid: I want to draw a line parallel to the bases (that is, parallel to and in between AD and BC) such that the top half and the bottom half both have equal area. Specifically, if we define the height of the trapezoid as 1, I want to know how far from …

Points G and H are midpoints of and in regular hexagon ABCDEF. If AB = 6 find GH. 13. The vertices of trapezoid ABCD are A(10, –1), B(6, 6), C(–2, 6), and D(–8, –1). Find … The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore, $16:(5 101 WT , if ZX = 20 and TY = 15 62/87,21 The trapezoid WXYZ is an isosceles trapezoid. So, the diagonals are congruent.

Find the value of y if AB = 2y — 7 and DC = 4y + 5, and EF=y+ 5 20 70, 12 24 a In trapezoid ABED, Il DC, and diagonal BD is drawn. Ifm < ABD = find: a) m < BDC Cs b) m < DB The cross section of an attic is in the shape of an isosceles trapezoid, as shown in the accompanying figure. 1. In the diagram below, ABCE is an isosceles trapezoid. Point D lies on line CE so that AE is parallel to BD and angle CBD=28 degrees Find angle BAE in degrees. ID: A 1 G.CO.C.11: Trapezoids 1a Answer Section 1 ANS: 4 REF: 061008ge 2 ANS: 2 Isosceles or not, RSV and RST have a common base, and since RS and VT are bases, congruent altitudes.

## 37. In isosceles trapezoid ABCD, AE = E 2x + 5, EC = 3x — 12, and BD = 4x + 20. Find the value of x. zx+5 +3x-lZC +x +2-0 Rd-ios ABCD PQRS 4x 4-20 Perimeter Ratio Volume Ratio AA— Similarity SSS— Similarity trapezoid PQRS. Justify your answer. Chapter 7 — Proportions & Similarity Vocabulary: Similarity ratio (scale factor) Area Ratio

Solving problems on isosceles trapezoids In this lesson you will find solutions of some typical problems on isosceles trapezoids. Reminder (see the lesson Trapezoids and their base angles under the current topic in this site).

### Determine whether ABCD is an isosceles trapezoid. Explain. find each measure. 45. AE. SOLUTION: The trapezoid PQRS is an isosceles trapezoid. So, the.

The area of the trapezoid is 33 … Get the answers you need, now! (a) Find the measure of a side of the rhombus. 152+82= ABCD is an isosceles trapezoid with AB CD and AD=BC. Find ABCD is a rectangle with diagonals AC AE ECF. 3.CP CTC. 22. In the diagram below, AHIJ and AHT J' are graphed This problem has been solved!

6) DA = CE and DC = AE, 6) By properties of parallelogram. 7) BC = 3) In trapezoid ABCD, ∠B= 120 0 Find
3 Isosceles trapezoid ABCD has diagonals AC and. BD. If AE = 5.2, AC = 11.7, and CD = 10.5, what is the feet, and AD = 28 feet, find the length of AB to the. Find m ∠l in rhombus GHJK. 32.The diagonals of square ABCD intersect at E. If AE = 2x + 6 and BD = 6x - 10, find AC.33.ABCD is an isosceles trapezoid with
ABCD, MZA = (2x + 10) and mZB = 3x.

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6) DA = CE and DC = AE, 6) By properties of parallelogram.

AE. DC. AE. A. D. B. E. C. 1. DC. AB. 6x y. 3x. 2.

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### Find the measures of the numbered angles in each isosceles trapezoid. Here, AB = CE (given) AE = CD (In rectangle opposite sides are equal) And, ∠ A E B. Source Code. That is If ZA Z D (or if LB Z C), then trapezoid ABCD is isosce

Isosceles trapezoids are dissected into three similar triangles and re-arranged to form two additional isosceles trapezoids. Moreover, triangle centers, one from each similar triangle, form the vertices of a centric triangle which has special properties.

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### Accordingly, in two triangles formed inside the trapezoid, it is necessary to find the sizes of the segments AE and DF. This can be done, for example, through the cosines of the angles A and D known to you.

Find the value of x. In isosceles trapezoid ABCD, AB Il DC, and AD = BC. EFis the median. Find the value of y if AB = 2y — 7 and DC = 4y + 5, and EF=y+ 5 20 70, 12 24 a In trapezoid ABED, Il DC, and diagonal BD is drawn.

## 13. For isosceles trapezoid MNOP F 44 64 14. The length of one base of a trapezoid is 19 inches and the length of the median is 16 inches. Find the length of the other base. 13 in 32 A 35 in. B 19 in. C 17.5 in. c 112 12 15. For kite PQRS, find mZS. 220 B 68 90 3Vo 16. ABCD is a parallelogram with coordinates A(4, 2), 13(4, —l), C(—2, —l), and D(—2, 2).

Ifm < ABD = find: a) m < BDC Cs b) m < DB The cross section of an attic is in the shape of an isosceles trapezoid, as shown in the accompanying figure. 1.

The area of the trapezoid student election sign is 5 square ft find two possible values for each base . Math The Isosceles Trapezoid and its Dissecting Similar Triangles Larry Hoehn Abstract. Isosceles trapezoids are dissected into three similar triangles and re-arranged to form two additional isosceles trapezoids. Moreover, triangle centers, one from each similar triangle, form the vertices of a centric triangle which has special properties. ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9, respectively. Angles ABC and BCD are both right angles.