Question

Decide whether the conditions create a unique triangle, multiple triangles, or no triangle

Given AABC.
m/A = 65°
m/B = 75°
m/C= 40°
OA. not enough information
OB. multiple triangles
OC. unique triangle
OD. no triangle

Answer 1

B. Multiple triangles

Explanation:

To determine whether the given conditions create a unique triangle, multiple triangles, or no triangle, we can apply the Triangle Sum Theorem. According to this theorem, the sum of the interior angles in a triangle is always 180°.

Calculate the sum of the given angles in triangle ABC:

m∠A + m∠B + m∠C = 65° + 75° + 40° = 180°

As the sum of the angles is equal to 180°, this satisfies the Triangle Sum Theorem and therefore a triangle can be formed with the given angle measurements.

Given only the angle measurements, we do not have enough information to determine the side lengths of triangle ABC. Without the side lengths, we cannot uniquely determine the triangle.

In similar triangles, the angles are congruent (the same), but the side lengths are proportional. Since the given angle measurements are fixed, we can create multiple triangles with different side lengths that satisfy those angles. These triangles will be similar to each other, meaning they have the same shape but different sizes.

Therefore, the correct answer is:

• B. Multiple triangles