Question

Given m₃ = m₄, prove that 1 and 2 are supplementary angles. Choose the correct reason for each statement.

a. Opposite angles, Definition of supplement, Substitution
b. Vertical angles, Complementary angles, Linear pair
c. Corresponding angles, Alternate interior angles, Same-side interior angles
d. Opposite rays, Transitive property, Alternate exterior angles

Answer 1

To prove that 1 and 2 are supplementary angles, use the property of vertical angles to show that angle 1 and angle 2 are congruent. Then, apply the definition of supplementary angles to prove that their measures add up to 180 degrees.

Step-by-step explanation:

In order to prove that 1 and 2 are supplementary angles, we need to show that their measures add up to 180 degrees. Given that m₃ = m₄, we can use the property of vertical angles to prove that 1 and 2 are supplementary.

Vertical angles are formed by two intersecting lines and are always congruent. In this case, angle 1 and angle 3 are vertical angles, and angle 2 and angle 4 are also vertical angles. Since m₃ = m₄, we can conclude that angle 1 and angle 2 are congruent.

According to the definition of supplementary angles, if two angles are supplementary, their measures add up to 180 degrees. Since angle 1 and angle 2 are congruent, their measures are equal. Therefore, the measure of angle 1 plus the measure of angle 2 is equal to 180 degrees, proving that they are supplementary angles.