Question

Complete the proofs that angle RUV is congruent to angle QRU.

a) Vertical angles are congruent.
b) Corresponding angles are congruent.
c) Alternate interior angles are congruent.
d) Supplementary angles are congruent.

Answer 1

To complete the proofs that angle RUV is congruent to angle QRU, we can use the property that vertical angles are congruent.

Step-by-step explanation:

To complete the proofs that angle RUV is congruent to angle QRU, we can use the following properties:

1. Vertical angles are congruent: Vertical angles are formed by two intersecting lines and are always congruent. Therefore, angle RUV and angle QRU are congruent.
2. Corresponding angles are congruent: Corresponding angles are formed when a transversal intersects two parallel lines. Since we don't have any parallel lines in the given information, we cannot use this property to prove the congruence.
3. Alternate interior angles are congruent: Alternate interior angles are formed when a transversal intersects two parallel lines. Since we don't have any parallel lines in the given information, we cannot use this property to prove the congruence.
4. Supplementary angles are congruent: Supplementary angles are two angles whose sum is 180 degrees. The given information does not provide any information about the measures of the angles, so we cannot use this property to prove the congruence.

Therefore, the only property that can be used to prove that angle RUV is congruent to angle QRU is that vertical angles are congruent.