Question

Fill in blank 3, 5, and 6. options; Linear Pairs Theorem ∠6 ≅ ∠7, ∠1 ≅ ∠7, Substitution Property of Equality, Transitive Property of Congruence.

a) ∠5, ∠1, Substitution Property of Equality
b) ∠7, ∠1, Linear Pairs Theorem
c) ∠6, ∠7, Transitive Property of Congruence
d) ∠6, ∠1, Transitive Property of Congruence

Answer 1

The correct fill in the blank option is d) °6, °1, Transitive Property of Congruence because this property states that if one angle is congruent to a second, and the second is congruent to a third, then the first and third are also congruent.

Step-by-step explanation:

To fill in the blank, one must apply the provided mathematical properties and theorems correctly to identify the relationship between the angles. Given that °6 ≅ °7 and °1 ≅ °7, we can use a property of equality or congruence to determine the relationship between °6 and °1.

One of the options must show that °6 is also congruent to °1 through a known property or theorem. The Transitive Property of Congruence is the property that states 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 also congruent. Therefore, the answer that uses the Transitive Property of Congruence to conclude that °6 is congruent to °1 is the correct choice.

The correct fill in the blank option from the given choices is thus:

• Option d) °6, °1, Transitive Property of Congruence