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Side Lengths: 2 cm, 2.4 cm, 3.6 cm
Angle Measures: 32°, 39°, 109°
Which choice describes another triangle that can be drawn?
Side Lengths: 2 cm, 2.4 cm, 3.6 cm
Angle Measures: 22°, 49°, 109°
Side Lengths: 6 cm, 7.2 cm, 10.8 cm
Angle Measures: 32°, 39°, 109°
Neither of these choices
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.