Statements Reasons

Question

1. m∡A+m∡C=180°
1. Linear Pairs are supplementary
2. m∡A=m∡E
2. __________________________
3.. m∡E+m∡C=180°
3. Substitution
4. ∠E and ∠C
are supplementary 4. Definition of Supplementary Angles


(1 point)
Responses

Definition of congruence
Definition of congruence

Corresponding Angles Postulate
Corresponding Angles Postulate

Transitive Property of Equality
Transitive Property of Equality

Vertical Angles Theorem

Answer 1

The correct response for the blank in statement 2 ("m∡A = m∡E") is:

Transitive Property of Equality

Here's the reasoning:

In the proof, you have m∡A = m∡C (from statement 1, combined with the fact that angles A and C are supplementary). Because m∡A = m∡E (statement 2) and m∡E + m∡C = 180° (statement 3), you can use the Transitive Property of Equality to show that if m∡A equals both m∡E and m∡C, then m∡E must also equal m∡C.

So, the completed statement 2 would read:

2. m∡C = m∡E (by Transitive Property of Equality)