Question

Provide reasons for the statements.
Given: ∠1 and ∠3 are vertical angles.
Prove: ∠1≅∠3
(Image below)

Answer 1

Ok, because angles are being added in #3, I think it would be supplementary angles.

Answer 2

Thank you, so you know about any of the others?

Answer 3

@lazorwolf64

Answer 4

This problem seems to be a form of logical proof, where each statement can be logically reasoned from one or more of the previous statements (or is a given, like the first statement).

I agree with Sailor, #3 is from the definition of supplementary angles
#4, I think could follow from the transitive property, i.e. a=b and b=c implies a=c. It's similar here. m1+m2 = 180; m2+m3= 180, this implies m1+m2 = m2+m3
From here, #5 is easy to derive my subtracting m2 from both sides of the equation in #4 m1+m2 = m2+m3
And if m1 = m3, then their angle measures should also be the same, though I'm not sure of the proper way to word this statement

Answer 5

Thank you so much!