Question

Draw two triangles that look similar and label them as ABC and DEF. Label one angle a Theo
sides of both triangles with numerical values such that the triangles are, in fact, similar. The scale factor of the sides needs to be 3/4.

Answer 1

Here are two similar triangles labeled ABC and DEF, with side lengths that reflect a scale factor of \( \frac{3}{4} \).

### Triangle ABC
- **Angle A = 30°**
- **Side AB = 8 units**
- **Side AC = 6 units**
- **Side BC = 10 units**

### Triangle DEF
- **Angle D = 30°** (Corresponding to Angle A)
- **Side DE = \( \frac{3}{4} \times 8 = 6 \) units**
- **Side DF = \( \frac{3}{4} \times 6 = 4.5 \) units**
- **Side EF = \( \frac{3}{4} \times 10 = 7.5 \) units**

### Triangle Correspondence
- **ABC ↔ DEF**
- **Angle A ↔ Angle D**
- **AB ↔ DE**
- **AC ↔ DF**
- **BC ↔ EF**

### Summary of the Triangles
- **Triangle ABC:**
- \( AB = 8 \)
- \( AC = 6 \)
- \( BC = 10 \)
- \( \angle A = 30° \)

- **Triangle DEF:**
- \( DE = 6 \)
- \( DF = 4.5 \)
- \( EF = 7.5 \)
- \( \angle D = 30° \)

Since the angles are equal and the sides are in the ratio \( \frac{3}{4} \), triangles ABC and DEF are similar by the Angle-Angle (AA) criterion for similarity.