part 5 of 10
write a proof of the triangle midsegment theorem.
given: $\overline{dg} \cong \overline{ge}$, $\overline{fh} \cong \overline{he}$
prove: $\overline{gh} \parallel \overline{df}$, $gh = \frac{1}{2}df$

what other angles are congruent?
$\bigcirc$ a. $\angle egh \cong \angle ehg$
$\bigcirc$ b. $\angle edf \cong \angle efd$
$\bigcirc$ c. $\angle egh \cong \angle edf$

Question

part 5 of 10
write a proof of the triangle midsegment theorem.
given: $\overline{dg} \cong \overline{ge}$, $\overline{fh} \cong \overline{he}$
prove: $\overline{gh} \parallel \overline{df}$, $gh = \frac{1}{2}df$

what other angles are congruent?
$\bigcirc$ a. $\angle egh \cong \angle ehg$
$\bigcirc$ b. $\angle edf \cong \angle efd$
$\bigcirc$ c. $\angle egh \cong \angle edf$

Accepted Answer

# Brief Explanations:
To prove the Triangle Midsegment Theorem, we use similarity and corresponding angles. $\angle EGH$ and $\angle EDF$ are corresponding angles formed by transversal $ED$ cutting through lines $GH$ and $DF$. For $GH \parallel DF$ (part of what we need to prove), these corresponding angles must be congruent. The other options do not represent congruent angles relevant to this proof: option A would imply an isosceles triangle which is not given, and option B would imply $	riangle EDF$ is isosceles which is not stated.
# Answer:
C. $\angle EGH \cong \angle EDF$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: