Help with 45? **Problem Set 5.4**---**Problems:****33.** Find the length of the legs in the following isosceles trapezoid. Round to the nearest hundredth.Diagram: A trapezoid with bases 6 inches and 10 inches, and height 4 inches.**34.** Find the area of the following isosceles trapezoid. Round to the nearest tenth.Diagram: A trapezoid with bases 7.8 meters and 8.5 meters, and height 10.6 meters.**35.** In isosceles trapezoid $ EFGH $, $ EF = 20'' $, $ FG = 25'' $, and $\angle H = 60^\circ$. Find $ EH $.Diagram: Not included.**36.** $ PQRS $ is an isosceles trapezoid. If $\angle TRS = 100^\circ$, $\angle T = 35^\circ$, and $ PS = TS $, find the measures of the numbered angles.Diagram: A trapezoid with angles marked as $4^\circ$, $3^\circ$, etc.**37.** In isosceles trapezoid $ WXYZ $, $ XP = 5 $ in., $ YZ = 12 $ in., $ XZ \perp WX $, and $ WY \perp YZ $. Find $ WZ $.Diagram: Trapezoid with diagonals intersecting at point P.---**Proofs:****39.** Prove: A square is a rhombus with one right angle.**40.** Prove: A square is a rectangle with two adjacent sides congruent.**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).**44.** Prove: The diagonals of an isosceles trapezoid are congruent.**45.** Prove: If the diagonals of a trapezoid are congruent, then it is an isosceles trapezoid.**46.** In parallelogram \(

Name: Help with 45? **Problem Set 5.4**---**Problems:****33.** Find the leng
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Description: Help with 45? **Problem Set 5.4**---**Problems:****33.** Find the length of the legs in the following isosceles trapezoid. Round to the nearest hundredth.Diagram: A trapezoid with bases 6 inches and 10 inches, and height 4 inches.**34.** Find the are

Prove:- if the diagonals of a trapezoid are congruent, then it is an isosceless trapeziod Now given is trapeziod ABCDAC≅BDDraw line CP throught C parallel to DB intersects AB extended at P DC∥AB BPCD is parallelogram [A parallelogram has two sets of parallel sides]BD≅PC [parallelogram has opposite sides congruent]AC≅PC [ given]△ACP is isosceless∠CAB≅∠CPB∠CPB≅∠DBA∠CAB≅∠DBA [given]now AB≅AB [Reflexive peroperty]△ACB≅△BDAso AD≅BChence it is an isosceles trapezoid

Answered: 45. Prove: If the diagonals of a…

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Help with 45?

**Problem Set 5.4**

---

**Problems:**

**33.** Find the length of the legs in the following isosceles trapezoid. Round to the nearest hundredth.

Diagram: A trapezoid with bases 6 inches and 10 inches, and height 4 inches.

**34.** Find the area of the following isosceles trapezoid. Round to the nearest tenth.

Diagram: A trapezoid with bases 7.8 meters and 8.5 meters, and height 10.6 meters.

**35.** In isosceles trapezoid $ EFGH $, $ EF = 20'' $, $ FG = 25'' $, and $\angle H = 60^\circ$. Find $ EH $.

Diagram: Not included.

**36.** $ PQRS $ is an isosceles trapezoid. If $\angle TRS = 100^\circ$, $\angle T = 35^\circ$, and $ PS = TS $, find the measures of the numbered angles.

Diagram: A trapezoid with angles marked as $4^\circ$, $3^\circ$, etc.

**37.** In isosceles trapezoid $ WXYZ $, $ XP = 5 $ in., $ YZ = 12 $ in., $ XZ \perp WX $, and $ WY \perp YZ $. Find $ WZ $.

Diagram: Trapezoid with diagonals intersecting at point P.

---

**Proofs:**

**39.** Prove: A square is a rhombus with one right angle.

**40.** Prove: A square is a rectangle with two adjacent sides congruent.

**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).

**44.** Prove: The diagonals of an isosceles trapezoid are congruent.

**45.** Prove: If the diagonals of a trapezoid are congruent, then it is an isosceles trapezoid.

**46.** In parallelogram \(

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