Side Lengths: 2 cm, 2.4 cm, 3.6 cm Angle Measures: 32°, 39°, 109° Which choice describes another triangle that can be drawn?

To determine if a triangle can be constructed with given side lengths and angle measures, we can apply the Triangle Inequality Theorem and the property that the sum of the angles in a triangle must equal 180°.

Examining the first triangle:

– Side Lengths: 2 cm, 2.4 cm, 3.6 cm (sum = 2 + 2.4 + 3.6 = 8 cm > 3.6 cm, satisfies the Triangle Inequality)

– Angle Measures: 32° + 39° + 109° = 180° (valid angle measures)

Now for the choices:
1. Side Lengths: 2 cm, 2.4 cm, 3.6 cm

– These sides correspond to the original triangle and are valid.

2. Side Lengths: 6 cm, 7.2 cm, 10.8 cm

– These lengths are proportional to the first triangle (multiply the sides by 3). So, they can also form a triangle.

– Angle measures (32°, 39°, 109°) also sum up to 180°.

Both choices would describe valid triangles since they meet the necessary conditions.

Thus, both triangles can be drawn.