Triangle Theorems and Angles Challenge

What is the sum of the interior angles of a triangle?

• 360 degrees

• 120 degrees

• 90 degrees

• 180 degrees

If two angles of a triangle are 45° and 55°, what is the measure of the third angle?

• 70°

• 80°

• 90°

• 100°

In triangle ABC, if angle A = angle B, what can you conclude about the sides of the triangle?

• Sides AC and BC are equal.

• Sides AB and AC are equal.

• Sides AB and BC are equal.

• All sides of the triangle are equal.

Calculate the measure of the exterior angle if one of the interior angles is 70°.

• 110°

• 90°

• 100°

• 120°

If triangle XYZ has angles measuring 30°, 30°, and 120°, is it isosceles? Why or why not?

• Yes, triangle XYZ is isosceles.

• Yes, triangle XYZ is equilateral.

• No, triangle XYZ has no equal angles.

• No, triangle XYZ is scalene.

Using the converse of the isosceles triangle theorem, if angle A = angle B, what can you conclude about the triangle?

• The triangle is equilateral.

• The triangle has no equal sides.

• The triangle is scalene.

• The triangle is isosceles.

In triangle DEF, if angle D = 40° and angle E = 60°, what is the measure of angle F?

• 80°

• 70°

• 90°

• 100°

What is the relationship between an exterior angle and the two opposite interior angles?

• The exterior angle is equal to the sum of the two opposite interior angles.

• The exterior angle is half the sum of the two opposite interior angles.

• The exterior angle is always greater than each of the opposite interior angles.

• The exterior angle is equal to the difference of the two opposite interior angles.

If triangle GHI is isosceles with base angles measuring 70°, what is the measure of the vertex angle?

• 30°

• 50°

• 40°

• 60°

Prove that triangle JKL is congruent to triangle MNO if angle J = angle M, angle K = angle N, and side JK = side MN.

• Triangle JKL is not congruent to triangle MNO.

• Triangle JKL has a larger area than triangle MNO.

• Triangle JKL is congruent to triangle MNO.

• Triangle JKL is similar to triangle MNO.