Click on the triangles that can be mapped onto APQR by a sequence of translations, rotations, reflections, or dilations. Select all that apply.

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
SectionP.CT: Test
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Question 30

**Problem 30: Transformation of Triangles**

Consider the triangle shown.

### Given Triangle:
A triangle \( \triangle PQR \) with the following dimensions:
- \( PQ \) = 12.8 cm
- \( PR \) = 18.6 cm
- \( \angle PQR \) = 114°
- \( \angle QPR \) = 36°

### Task:
Click on the triangles that can be mapped onto \( \triangle PQR \) by a sequence of translations, rotations, reflections, or dilations. Select all that apply.

### Candidate Triangles:
1. **Triangle \( \triangle KLM \) (Top-Left)**
   - \( KL \) = 9.3 cm
   - \( \angle L \) = 114°
   - \( \angle K \) = 30°
   - \( \angle M \) = 36°
 
2. **Triangle \( \triangle KLM \) (Top-Right)**
   - \( KM \) = 9.3 cm
   - \( ML \) = 6.4 cm
   - \( \angle K \) = 36°
   - \( \angle M \) = 30°
   - \( \angle L \) = 114°
 
3. **Triangle \( \triangle LKM \) (Middle-Left)**
   - \( LK \) = 6.4 cm
   - \( LM \) = 9.3 cm
   - \( \angle L \) = 46°
   - \( \angle K \) = 30°

4. **Triangle \( \triangle KLM \) (Middle-Right)**
   - \( KM \) = 6.4 cm
   - \( LK \) = 9.3 cm
   - \( \angle K \) = 31°
   - \( \angle M \) = 114°

5. **Triangle \( \triangle LKM \) (Bottom-Left)**
   - \( LK \) = 9.3 cm
   - \( KM \) = 9.3 cm
   - \( \angle L \) = 114°
   - \( \angle M \) = 30°

6. **Triangle \( \triangle KLM \) (Bottom-Right)**
   - \( KL \) = 9.3
Transcribed Image Text:**Problem 30: Transformation of Triangles** Consider the triangle shown. ### Given Triangle: A triangle \( \triangle PQR \) with the following dimensions: - \( PQ \) = 12.8 cm - \( PR \) = 18.6 cm - \( \angle PQR \) = 114° - \( \angle QPR \) = 36° ### Task: Click on the triangles that can be mapped onto \( \triangle PQR \) by a sequence of translations, rotations, reflections, or dilations. Select all that apply. ### Candidate Triangles: 1. **Triangle \( \triangle KLM \) (Top-Left)** - \( KL \) = 9.3 cm - \( \angle L \) = 114° - \( \angle K \) = 30° - \( \angle M \) = 36° 2. **Triangle \( \triangle KLM \) (Top-Right)** - \( KM \) = 9.3 cm - \( ML \) = 6.4 cm - \( \angle K \) = 36° - \( \angle M \) = 30° - \( \angle L \) = 114° 3. **Triangle \( \triangle LKM \) (Middle-Left)** - \( LK \) = 6.4 cm - \( LM \) = 9.3 cm - \( \angle L \) = 46° - \( \angle K \) = 30° 4. **Triangle \( \triangle KLM \) (Middle-Right)** - \( KM \) = 6.4 cm - \( LK \) = 9.3 cm - \( \angle K \) = 31° - \( \angle M \) = 114° 5. **Triangle \( \triangle LKM \) (Bottom-Left)** - \( LK \) = 9.3 cm - \( KM \) = 9.3 cm - \( \angle L \) = 114° - \( \angle M \) = 30° 6. **Triangle \( \triangle KLM \) (Bottom-Right)** - \( KL \) = 9.3
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