Question

In the figure, p || q. You must prove that ∠4 is supplementary to ∠7. What is the reason for the highlighted statement in the proof?

Substitution Property of Equality

For parallel lines cut by a transversal, corresponding angles are congruent.

Congruent Supplements Theorem

Vertical Angles Theorem

Answer 1

Here's the figure.

Answer 2

@bibby

Answer 3

My guess was B

Answer 4

corresponding angles would be 4 and 8 I believe

Answer 5

Oh, then would it be C?

Answer 6

<2+<4=180
<2=<7
<7+<4-=180

I think this would be Substitution Property of Equality

Answer 7

Substitution Property of Equality

Answer 8

Oh, thank you! :)

Answer 9

There is a small mistake in the proof.
The statement above the highlighted statement states: <2 = <7
It should state: m<2 = m<7
The m's (for measure) were left out.

Answer 10

what's the difference?

Answer 11

I guess stating <2=<7 makes no sense actually

Answer 12

This is a small error, but geometry proofs are formal proofs and congruence and equality are different.
Notice that two statements above the highlighted statement it states: <2 =~ <7 (the angles are congruent)
The statement below uses the definition of congruent angles, so the statement is that the measures are equal, not that the angles are equal. In fact, the angles are not equal. It is only the measures that are equal.
In order to use substitution, you must have previous statements stating equality of measures.

Answer 13

In geometry, something is only equal to itself. Two different angles with the same measure are congruent angles, not equal angles. The same goes for two congruent segments. Unless the two congruent segments are the same segment, they are congruent, but not equal.

Answer 14

I've learned something today. Thank you!

Answer 15

You're welcome.
Good job, btw; you got it right before me.