Question

Fill in the blanks using the given options: Linear Pairs Theorem, ∠6 ≅ ∠7, ∠1 ≅ ∠7, Substitution Property of Equality, Transitive Property of Congruence.

If ∠6 and ∠1 are supplementary, and ∠1 ≅ ∠7, then by the ________, ∠6 ≅ ________.

a) Linear Pairs Theorem, ∠7
b) ∠6 ≅ ∠7, Substitution Property of Equality
c) Transitive Property of Congruence, ∠7
d) Substitution Property of Equality, Linear Pairs Theorem

Answer 1

The correct fill-in-the-blank answer is the Transitive Property of Congruence, which concludes that angle 6 is congruent to angle 7.

Step-by-step explanation:

If ∠6 and ∠1 are supplementary, and ∠1 ≅ ∠7, then by the Transitive Property of Congruence, ∠6 ≅ ∠7. The Transitive Property of Congruence states that if one angle is congruent to a second angle, and the second angle is congruent to a third angle, then the first and third angles are congruent. Since angles 6 and 1 are supplementary, they add up to 180 degrees.

The fact that angle 1 is congruent to angle 7 means that they have the same measure. By the Transitive Property, angles 6 and 7 must also have the same measure, thus ∠6 ≅ ∠7.