## 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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Answered: Which statement must be true? 20 15

Math

Geometry

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

Problem 1CT

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

## 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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