Question

5 fill in the blank 1 point given: $overline{hm}congoverline{de}$ prove: $gh + de=gm$ complete the proof below. statements reasons 1 $gh + hm = gm$ 1 choose your answer. 2 $overline{hm}congoverline{de}$ 2 choose your answer. 3 choose your answer. 3 angle addition postulate segment addition postulate 4 choose your answer. 4 midpoint theorem

Explanation:

Step1: Segment - addition principle

By the Segment Addition Postulate, since points $G$, $H$, and $M$ are collinear, we have $GH + HM=GM$.

Step2: Given information

We are given that $\overline{HM}\cong\overline{DE}$, which means $HM = DE$.

Step3: Substitution

Substitute $HM$ with $DE$ in the equation $GH + HM=GM$. So, $GH + DE=GM$.

Answer:

1. Segment Addition Postulate
2. Given
3. $GH + DE=GM$; Substitution Property of Equality
4. N/A (not required as the proof is complete with the above - steps)