Determine if the triangles are similar. If so, write a similarity statement. ### Determine whether the triangles are similar. If they are, write a similarity statement.**Problem:** 33.**Diagrams:**1. **First Triangle (ABC):** - Side AB: 12 units - Side BC: 10 units - Side AC: 6 units2. **Second Triangle (DEF):** - Side DE: 6 units - Side EF: $7 \frac{1}{5}$ units (or $7.2$ units) - Angle D at vertex DEF: $33^\circ 33' 53''$**Solution Steps:**1. **Check angles:** - Measure the angles of both triangles to see if any pairs of corresponding angles are congruent. We can compare the given angles: - First triangle (ABC) does not have any angle measures listed. - Second triangle (DEF) lists one angle at vertex D: $33^\circ 33' 53''$.2. **Check sides:** - Compare the corresponding sides of both triangles to see if their ratios are equal. - Calculate the ratios of corresponding sides of triangles ABC and DEF: - AB / DE = 12 / 6 = 2 - BC / EF = 10 / 7.2 ≈ 1.39 - AC / DF: We do not have the measure for side DF.2. Since not all ratios of corresponding sides are equal, **the triangles are not similar.**

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Answered: Determine whether the triangles are…

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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Determine if the triangles are similar. If so, write a similarity statement.

### Determine whether the triangles are similar. If they are, write a similarity statement.

**Problem:** 33.

**Diagrams:**

1. **First Triangle (ABC):**
- Side AB: 12 units
- Side BC: 10 units
- Side AC: 6 units

2. **Second Triangle (DEF):**
- Side DE: 6 units
- Side EF: $7 \frac{1}{5}$ units (or $7.2$ units)
- Angle D at vertex DEF: $33^\circ 33' 53''$

**Solution Steps:**

1. **Check angles:**
- Measure the angles of both triangles to see if any pairs of corresponding angles are congruent. We can compare the given angles:
- First triangle (ABC) does not have any angle measures listed.
- Second triangle (DEF) lists one angle at vertex D: $33^\circ 33' 53''$.

2. **Check sides:**
- Compare the corresponding sides of both triangles to see if their ratios are equal.
- Calculate the ratios of corresponding sides of triangles ABC and DEF:
- AB / DE = 12 / 6 = 2
- BC / EF = 10 / 7.2 ≈ 1.39
- AC / DF: We do not have the measure for side DF.

2. Since not all ratios of corresponding sides are equal, **the triangles are not similar.**

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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