Supply the missing steps in the following paragraph proof.
Given: ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary
Prove: ∠1 ≈∠3
By the definition of supplementary angles, m∠1 + m∠2 = 180˚ and
m∠2 + m∠3 = 180˚. (did I get 180 right on these two)
Then, m∠1 + m∠2 = m∠2 + m∠3 by_______________.
Subtract m∠2 from each side. You get m∠1 = _____ or ∠1 ≈______.
I can't figure out the rest
HELPPP!!
i think i got it idk
Then, m∠1 + m∠2 = m∠2 + m∠3 by the substitution property.
Subtract m∠2 from each side. You get m∠1 m∠3 = or ∠1 ≈ m∠3.
To supply the missing steps in the paragraph proof, we need to show how to obtain the result m∠1 = m∠3 or ∠1 ≈ ∠3 from the given information.
Since we have m∠1 + m∠2 = 180˚ and m∠2 + m∠3 = 180˚ (which you have correctly stated), we know that the sum of the angles in a straight line is 180˚. Therefore, we can conclude that m∠1 + m∠2 = m∠2 + m∠3 by the Transitive Property of Equality.
The Transitive Property of Equality allows us to equate the sums of the angles because if two quantities are equal to a third quantity separately, then they must be equal to each other as well.
Now, to prove ∠1 ≈ ∠3, we subtract m∠2 from each side of the equation m∠1 + m∠2 = m∠2 + m∠3:
m∠1 + m∠2 - m∠2 = m∠2 + m∠3 - m∠2
This simplifies to:
m∠1 = m∠3.
Therefore, we have shown that ∠1 ≈ ∠3, or in other words, ∠1 and ∠3 are congruent.