In isosceles trapezoid WXYZ, XP = 5 in., YZ = 12 in., XZ 1 WX, and WY 1 YZ Find WZ. P. W

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**Problem Set 5.4**

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**Geometry Problems**

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

Trapezoid Illustration:

- Base 1: 6"
- Height: 4"
- Base 2: 10"

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

Trapezoid Illustration:

- Base 1: 7.8 m
- Height: 8.5 m
- Base 2: 10.6 m

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

**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.

Trapezoid Illustration:

- Angle \(\angle T\): 35°
- Angle \(\angle TRS\): 100°

**37.** In isosceles trapezoid \(WXYZ\), \(XP = 5 \, \text{in.}\), \(YZ = 12 \, \text{in.}\), \(XZ \perp WX\), and \(WY \perp YZ\). Find \(WZ\).

Trapezoid Illustration:

- Segments: \(XP = 5\), \(YZ = 12\)

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**Geometry 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 diagon
Transcribed Image Text:**Problem Set 5.4** --- **Geometry Problems** **33.** Find the length of the legs in the following isosceles trapezoid. Round to the nearest hundredth. Trapezoid Illustration: - Base 1: 6" - Height: 4" - Base 2: 10" **34.** Find the area of the following isosceles trapezoid. Round to the nearest tenth. Trapezoid Illustration: - Base 1: 7.8 m - Height: 8.5 m - Base 2: 10.6 m **35.** In isosceles trapezoid \(EFGH\), \(EF = 20''\), \(FG = 25''\), and \(\angle H = 60^\circ\). Find \(EH\). **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. Trapezoid Illustration: - Angle \(\angle T\): 35° - Angle \(\angle TRS\): 100° **37.** In isosceles trapezoid \(WXYZ\), \(XP = 5 \, \text{in.}\), \(YZ = 12 \, \text{in.}\), \(XZ \perp WX\), and \(WY \perp YZ\). Find \(WZ\). Trapezoid Illustration: - Segments: \(XP = 5\), \(YZ = 12\) --- **Geometry 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 diagon
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