Question

Each row of the table shows two of the interior angle measures of two triangles.

Which triangles are similar?

Choose Similar or Not Similar for each pair of triangles.



Triangles Similar Not Similar
Triangle 1: 32°, 40°

Triangle 2: 108°, 60°



Triangle 1: 94°, 64°

Triangle 2: 22°, 64°



Triangle 1: 70°, 80°

Triangle 2: 70°, 20°

Answer 1

To determine whether the triangles are similar, we can use the Angle-Angle (AA) similarity criterion, which states that if two triangles have two angles that are equal, then the triangles are similar.

To compare the angles of the triangles:

1. **Triangle 1: 32°, 40°**
- The third angle can be calculated as: 180° - (32° + 40°) = 180° - 72° = 108°.
- Angles are 32°, 40°, and 108°.

**Triangle 2: 108°, 60°**
- The third angle can be calculated as: 180° - (108° + 60°) = 180° - 168° = 12°.
- Angles are 108°, 60°, and 12°.

- **Not Similar** (no angles are the same).

2. **Triangle 1: 94°, 64°**
- The third angle can be calculated as: 180° - (94° + 64°) = 180° - 158° = 22°.
- Angles are 94°, 64°, and 22°.

**Triangle 2: 22°, 64°**
- The third angle can be calculated as: 180° - (22° + 64°) = 180° - 86° = 94°.
- Angles are 22°, 64°, and 94°.

- **Similar** (all angles match: 94°, 64°, and 22°).

3. **Triangle 1: 70°, 80°**
- The third angle can be calculated as: 180° - (70° + 80°) = 180° - 150° = 30°.
- Angles are 70°, 80°, and 30°.

**Triangle 2: 70°, 20°**
- The third angle can be calculated as: 180° - (70° + 20°) = 180° - 90° = 90°.
- Angles are 70°, 20°, and 90°.

- **Not Similar** (no angles are the same).

To summarize:
- Triangle 1 (32°, 40°) & Triangle 2 (108°, 60°): **Not Similar**
- Triangle 1 (94°, 64°) & Triangle 2 (22°, 64°): **Similar**
- Triangle 1 (70°, 80°) & Triangle 2 (70°, 20°): **Not Similar**