Move words to the blanks and equations to the boxes to prove that vertical angles <1 and <3 are congruent

Because linear pairs are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.

Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.

Step-by-step explanation:

A linear pair is a pair of adjacent angles formed when two lines intersect. The two angles of a linear pair are always supplementary (that is they add up to 180°).

Therefore m∠1 and m∠2 are linear pairs, also m∠2 and m∠3 are linear pairs.

Hence:

m∠1 + m∠2 = 180°

m∠2 + m∠3 = 180°

Using substitution property:

m∠1 + m∠2 = m∠2 + m∠3

subtracting m∠2 from both sides:

m∠1 + m∠2 - m∠2 = m∠2 + m∠3 - m∠2

m∠1 = m∠3

∠1 and ∠2 are congruent

Because linear pairs are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.

Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.