If the diagonals of a trapezoid are congruent, what can If two of the base angles of a trapezoid are congruent,

24. The state of Nevada

approximates the shape of a trapezoid with these dimensions for boundaries: 340 miles on the north, 515 miles on the east, 435 miles on the south, and 225 miles on the west. If A and B are points located midway across the north and south boundaries, what is the approximate distance from A to B?

35. In the figure for Exercise 33, suppose that and

. Find: a AB c EF b DC d Whether

36. Given:

and bisects Find:

37. In a gambrel style roof, the gable end of a barn has the

shape of an isosceles trapezoid surmounted by an isosceles triangle. If and , find: a AS b VD c CD d DE BD = 24 ft AE = 30 ft m ∠FCE ∠DCB CF CE ‘ DA m ∠A = m∠B = 56° AB ‘ DC EF = 1 2 AB + DC MF = 3.5 EM =

7.1

39. The vertical sidewall of an

in-ground pool that is 24 ft in length has the shape of a trapezoid. What is the depth of the pool in the middle?

40. For the in-ground pool shown in Exercise 39, find the

length of the sloped bottom from point D to point C.

41. In trapezoid ABCD not shown, ,

, and . Find all possible values of x.

42. In trapezoid ABCD, and . If

, , and , find the perimeter of . 䉭DAC BC = 8 AB = 6 DA = 17 BC ⬜ AC BC ⬜ AB m ∠C = x 5 + 50 m ∠B = x 3 + 50 m ∠A = x 2 + 10

38. Successive steps on a ladder form isosceles

trapezoids with the sides. and . a Find GN, the width of the bottom step b Which step is the median of the trapezoid with bases and ? GN AH BI = 2.125 ft AH = 2 ft For Exercises 34 and 35, is the median of trapezoid ABCD.

34. In the figure for Exercise 33, suppose that and

. Find: a MF c EF b EM d Whether EF = 1 2 AB + DC DC = 18.4 AB = 12.8 EF

26. In the figure, and B is the midpoint of

. If , , , and , find x and y. In Exercises 27 to 33, complete a formal proof. 27. The diagonals of an isosceles trapezoid are congruent. 28. The median of a trapezoid is parallel to each base.

29. If two consecutive angles of a quadrilateral are

supplementary, the quadrilateral is a trapezoid.

30. If two base angles of a trapezoid are congruent, the

trapezoid is an isosceles trapezoid.

31. If three parallel lines intercept congruent segments on one

transversal, then they intercept congruent segments on any transversal.

32. If the midpoints of the sides of an isosceles trapezoid

are joined in order, then the quadrilateral formed is a rhombus.

33. Given: is the median of trapezoid ABCD

Prove: HINT: Using Theorem 4.4.7, show that M is the midpoint of . For ADC and CBA, apply Theorem 4.2.5. 䉭 䉭 AC EF = 1 2 AB + DC EF EF = 5x - y + 2 DE = 2x + 3y + 3 BC = x + y + 7 AB = 2x + 3y AC a ‘ b ‘ c

25. In the figure, a b c and B is

the midpoint of . If , , and , find the length of . EF DE = 3x + 2 BC = x + 7 AB = 2x + 3 AC ‘ ‘ 435 mi 340 mi 515 mi 225 mi NEVADA A B A B C a b c F E D Exercises 25, 26 A M B C D E F Exercises 33–35 B C D E A S T V 5 ft 8 ft A E F B D C A H B I C J D K E L F M G N 3 24 A D B C 13