45. Prove: If the diagonals of a trapezoid are congru- ent, then it is an isosceles trapezoid.

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Problem Set 5.4 277
33. Find the length of the legs in the following isosceles
trapezoid. Round to the nearest hundredth.
6"
18
10"
57
34. Find the area of the following isosceles trapezoid.
Round to the nearest tenth.
PROOFS
7.8 m
39. Prove: A square is a rhombus with one right angle.
40. Prove: A square is a rectangle with two adjacent
sides congruent.
8.5 m
41. Prove: A square is a rhombus with congruent
diagonals.
42. Prove: A square is a rectangle with perpendicular
diagonals.
43. Prove: A parallelogram with one right angle is a
rectangle (Theorem 5.27).
106 m
35. In isosceles trapezoid EFGH,EF = 20", FG = 25",
and ZH = 60°, Find EH.
44. Prove: The diagonals of an isosceles trapezoid are
congruent.
36. PQRS is an isosceles trapezoid. If ZTRS = 100°,
ZT = 35°, and PS = TS, find the measures of the
numbered angles.
45. Prove: If the diagonals of a trapezoid are congru-
ent, then it is an isosceles trapezoid.
46. In parallelogram ABCD, BP and CQ are altitudes.
Prove that PBCQ is a rectangle.
B
R
4
APPLICATIONS
37. In isosceles trapezoid WXYZ, X P = 5 in., Y Z =
12 in., XZ 1 WX, and WY 1 YZ Find WZ.
47. While building the frame for a new door, you mea-
sure to determine if the frame is a rectangle. For
each of the following situations, explain whether
you can conclude the frame is a rectangle.
a. You measure and find opposite sides are the
same length.
b. You measure and determine both diagonals are
the same length.
c. You measure one angle and determine it is a
Transcribed Image Text:Problem Set 5.4 277 33. Find the length of the legs in the following isosceles trapezoid. Round to the nearest hundredth. 6" 18 10" 57 34. Find the area of the following isosceles trapezoid. Round to the nearest tenth. PROOFS 7.8 m 39. Prove: A square is a rhombus with one right angle. 40. Prove: A square is a rectangle with two adjacent sides congruent. 8.5 m 41. Prove: A square is a rhombus with congruent diagonals. 42. Prove: A square is a rectangle with perpendicular diagonals. 43. Prove: A parallelogram with one right angle is a rectangle (Theorem 5.27). 106 m 35. In isosceles trapezoid EFGH,EF = 20", FG = 25", and ZH = 60°, Find EH. 44. Prove: The diagonals of an isosceles trapezoid are congruent. 36. PQRS is an isosceles trapezoid. If ZTRS = 100°, ZT = 35°, and PS = TS, find the measures of the numbered angles. 45. Prove: If the diagonals of a trapezoid are congru- ent, then it is an isosceles trapezoid. 46. In parallelogram ABCD, BP and CQ are altitudes. Prove that PBCQ is a rectangle. B R 4 APPLICATIONS 37. In isosceles trapezoid WXYZ, X P = 5 in., Y Z = 12 in., XZ 1 WX, and WY 1 YZ Find WZ. 47. While building the frame for a new door, you mea- sure to determine if the frame is a rectangle. For each of the following situations, explain whether you can conclude the frame is a rectangle. a. You measure and find opposite sides are the same length. b. You measure and determine both diagonals are the same length. c. You measure one angle and determine it is a
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