Which statement must be true? 20 15

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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## Beginning-of-Year Assessment

### Due 06/16/21 11:59pm

---

**1. Which statement must be true?**

![Two triangles labeled with given side lengths and angles.](image1)

- Triangle with angles labeled as x and sides 15 and 20 respectively.
- Triangle with angles labeled as y and sides 20 and an unknown side.

**Options:**
- A. \( x < y \)
- B. \( x = y \)
- C. \( y < x \)
- D. No relationship between \( x \) and \( y \) can be determined from the information given.

---

**2. What is \( \angle JLK \)?**

![Triangle JLK with angle J labeled 46 degrees. Sides LJ and JK are indicated to be equal.](image2)

**Explanation:**
- The diagram shows triangle \( \triangle JLK \) with angle \( J = 46^\circ \). Sides \( LJ \) and \( JK \) are marked as equal.

**Question:**
- Calculate the measure of \( \angle JLK \).

---

**3. Which angles are congruent to \( \angle 3 \)?**

![Parallel lines with multiple angles labeled.](image3)

**Explanation:**
- The diagram features two parallel lines intersecting with a transversal, creating multiple angles labeled 1 through 8.

**Options:**
- Determine which angles are congruent to \( \angle 3 \).

---

**4. A circle has center (5, -4) and radius 8. Which gives the equation for the circle?**

**Options:**
- A. \( (x + 5)^2 + (y - 4)^2 = 8 \)
- B. \( (x - 5)^2 + (y + 4)^2 = 8 \)
- C. \( (x + 5)^2 + (y - 4)^2 = 64 \)
- D. \( (x - 5)^2 + (y + 4)^2 = 64 \)

---

### Graph and Diagram Explanation:

1. **Triangle Comparison:**
   - Two triangles are shown with given sides. One triangle has sides labeled 15 and 20 with angle \( x \) opposite side 15. The other has side 20 with angle \( y \) opposite this side. The relationships between
Transcribed Image Text:## Beginning-of-Year Assessment ### Due 06/16/21 11:59pm --- **1. Which statement must be true?** ![Two triangles labeled with given side lengths and angles.](image1) - Triangle with angles labeled as x and sides 15 and 20 respectively. - Triangle with angles labeled as y and sides 20 and an unknown side. **Options:** - A. \( x < y \) - B. \( x = y \) - C. \( y < x \) - D. No relationship between \( x \) and \( y \) can be determined from the information given. --- **2. What is \( \angle JLK \)?** ![Triangle JLK with angle J labeled 46 degrees. Sides LJ and JK are indicated to be equal.](image2) **Explanation:** - The diagram shows triangle \( \triangle JLK \) with angle \( J = 46^\circ \). Sides \( LJ \) and \( JK \) are marked as equal. **Question:** - Calculate the measure of \( \angle JLK \). --- **3. Which angles are congruent to \( \angle 3 \)?** ![Parallel lines with multiple angles labeled.](image3) **Explanation:** - The diagram features two parallel lines intersecting with a transversal, creating multiple angles labeled 1 through 8. **Options:** - Determine which angles are congruent to \( \angle 3 \). --- **4. A circle has center (5, -4) and radius 8. Which gives the equation for the circle?** **Options:** - A. \( (x + 5)^2 + (y - 4)^2 = 8 \) - B. \( (x - 5)^2 + (y + 4)^2 = 8 \) - C. \( (x + 5)^2 + (y - 4)^2 = 64 \) - D. \( (x - 5)^2 + (y + 4)^2 = 64 \) --- ### Graph and Diagram Explanation: 1. **Triangle Comparison:** - Two triangles are shown with given sides. One triangle has sides labeled 15 and 20 with angle \( x \) opposite side 15. The other has side 20 with angle \( y \) opposite this side. The relationships between
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