2. Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain. A. В. 6. 88 8. D 490 6. 6. 43 8 4 12 49 10 H. 4. U 3 T
2. Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain. A. В. 6. 88 8. D 490 6. 6. 43 8 4 12 49 10 H. 4. U 3 T
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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Transcribed Image Text:### Determining Polygon Similarity
#### Task:
Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.
#### A. Rectangles
- **Rectangle LMON:**
- LM = 4
- ON = 10
- **Rectangle RSTU:**
- RS = 8
- UT = 3
**Analysis:**
- Compare side ratios:
- LM/RS = 4/8 = 1/2
- ON/UT = 10/3
- The side ratios are not equal, so the rectangles are not similar.
#### B. Triangles
- **Triangle DBC:**
- DB = 6
- BC = 9
- DC = 12
- ∠D = 49°
- ∠B = 88°
- **Triangle HIJ:**
- HI = 6
- IJ = 8
- HJ = 4
- ∠H = 43°
- ∠I = 49°
**Analysis:**
- Compare angles:
- ∠D (49°) with ∠I (49°)
- The given angles do not correspond, and the triangles have different sets of angles; hence, they are not similar.
### Conclusion:
Neither pair of polygons is similar because neither meets the criteria for similarity: equal corresponding angles and proportional corresponding sides.
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