5. The figure below is a square. Fill in the indicated information. E а. тZEHT b. m/HCA=[ H c. EH 8 m

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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**Mathematics - Geometry Exercise: Squares and Angles**

**Problem Statement:**
Examine the figure below, which is a square labeled \( EATC \). Complete the tasks by filling in the indicated information on the right.

**Diagram Explanation:**
- The square is named \( EATC \) with vertices \( E, A, T, \) and \( C \) listed in clockwise order.
- Inside the square, diagonals \( ET \) and \( AC \) intersect at point \( H \).
- One side of the square \( TC \) is marked as 8 meters.
- The corners of the square are right angles (90°).

**Tasks:**
a. \( m\angle EHT \) = \_\_\_\_\_\_\_\_ (degrees)

b. \( m\angle HCA \) = \_\_\_\_\_\_\_\_ (degrees)

c. \( EH \) = \_\_\_\_\_\_\_\_ (meters)

d. \( AT \) = \_\_\_\_\_\_\_\_ (meters)

e. \( ET \) = \_\_\_\_\_\_\_\_ (meters)

To solve this problem:

1. Review the properties of squares and their diagonals.
2. Recall that diagonals of a square bisect each other at right angles.
3. Apply knowledge of right-angle triangles and the Pythagorean theorem to find needed lengths.

---

This exercise helps in understanding geometrical properties and applying them to solve for angles and lengths within a square.
Transcribed Image Text:**Mathematics - Geometry Exercise: Squares and Angles** **Problem Statement:** Examine the figure below, which is a square labeled \( EATC \). Complete the tasks by filling in the indicated information on the right. **Diagram Explanation:** - The square is named \( EATC \) with vertices \( E, A, T, \) and \( C \) listed in clockwise order. - Inside the square, diagonals \( ET \) and \( AC \) intersect at point \( H \). - One side of the square \( TC \) is marked as 8 meters. - The corners of the square are right angles (90°). **Tasks:** a. \( m\angle EHT \) = \_\_\_\_\_\_\_\_ (degrees) b. \( m\angle HCA \) = \_\_\_\_\_\_\_\_ (degrees) c. \( EH \) = \_\_\_\_\_\_\_\_ (meters) d. \( AT \) = \_\_\_\_\_\_\_\_ (meters) e. \( ET \) = \_\_\_\_\_\_\_\_ (meters) To solve this problem: 1. Review the properties of squares and their diagonals. 2. Recall that diagonals of a square bisect each other at right angles. 3. Apply knowledge of right-angle triangles and the Pythagorean theorem to find needed lengths. --- This exercise helps in understanding geometrical properties and applying them to solve for angles and lengths within a square.
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