# SOLUTION: The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore,

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1 Find each measure. 1. The trapezoid ABCD is an isosceles trapezoid. So, each pair of base angles is congruent. Therefore, 2. WT, if ZX = 20 and TY = 15 The trapezoid WXYZ is an isosceles trapezoid. So, the diagonals are congruent. Therefore, WY = ZX. WT + TY = ZX WT + 15 = 20 WT = 5 esolutions Manual - Powered by Cognero Page 1

2 COORDINATE GEOMETRY Quadrilateral ABCD has vertices A ( 4, 1), B( 2, 3), C(3, 3), and D(5, 1). 3. Verify that ABCD is a trapezoid. First graph the points on a coordinate grid and draw the trapezoid. Use the slope formula to find the slope of the sides of the trapezoid. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral ABCD is a trapezoid. esolutions Manual - Powered by Cognero Page 2

3 4. Determine whether ABCD is an isosceles trapezoid. Explain. Refer to the graph of the trapezoid. Use the slope formula to find the slope of the sides of the quadrilateral. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral ABCD is a trapezoid. Use the Distance Formula to find the lengths of the legs of the trapezoid. The lengths of the legs are equal. Therefore, ABCD is an isosceles trapezoid. esolutions Manual - Powered by Cognero Page 3

4 CCSS SENSE-MAKING If ABCD is a kite, find each measure. 7. A is an obtuse angle and C is an acute angle. Since a kite can only have one pair of opposite congruent angles and The sum of the measures of the angles of a quadrilateral is 360. Find each measure. 9. The trapezoid QRST is an isosceles trapezoid so each pair of base angles is congruent. So, The sum of the measures of the angles of a quadrilateral is 360. Let m Q = m T = x. So, esolutions Manual - Powered by Cognero Page 4

5 11. PW, if XZ = 18 and PY = 3 The trapezoid WXYZ is an isosceles trapezoid. So, the diagonals are congruent. Therefore, YW = XZ. YP + PW = XZ. 3 + PW = 18 PW = 15 esolutions Manual - Powered by Cognero Page 5

6 COORDINATE GEOMETRY For each quadrilateral with the given vertices, verify that the quadrilateral is a trapezoid and determine whether the figure is an isosceles trapezoid. 13. J( 4, 6), K(6, 2), L(1, 3), M( 4, 1) First graph the trapezoid. Use the slope formula to find the slope of the sides of the quadrilateral. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral JKLM is a trapezoid. Use the Distance Formula to find the lengths of the legs of the trapezoid. The lengths of the legs are not equal. Therefore, JKLM is not an isosceles trapezoid. esolutions Manual - Powered by Cognero Page 6

7 15. W( 5, 1), X( 2, 2), Y(3, 1), Z(5, 3) First graph the trapezoid. Use the slope formula to find the slope of the sides of the quadrilateral. The slopes of exactly one pair of opposite sides are equal. So, they are parallel. Therefore, the quadrilateral WXYZ is a trapezoid. Use the Distance Formula to find the lengths of the legs of the trapezoid. The lengths of the legs are not equal. Therefore, WXYZ is not an isosceles trapezoid. esolutions Manual - Powered by Cognero Page 7

8 For trapezoid QRTU, V and S are midpoints of the legs. 17. If QR = 4 and UT = 16, find VS. By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. are the bases and is the midsegment. So, 19. If TU = 26 and SV = 17, find QR. By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. are the bases and is the midsegment. So, 21. If RQ = 5 and VS = 11, find UT. By the Trapezoid Midsegment Theorem, the midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. are the bases and is the midsegment. So, esolutions Manual - Powered by Cognero Page 8

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