Question

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 is a known fact about similar triangles? select all that apply.
a. corresponding sides of similar triangles are proportional.
b. corresponding angles of similar triangles are not equal, but proportional.
c. corresponding angles of similar triangles are congruent.
d. corresponding sides of similar triangles are congruent.

Explanation:

• For option A: A defining property of similar triangles is that their corresponding sides maintain a constant proportional ratio.
• For option B: This is incorrect because corresponding angles of similar triangles are equal (congruent), not proportional.
• For option C: Congruent corresponding angles are a key characteristic of similar triangles, as angle equality is required for similarity.
• For option D: This describes congruent triangles, not similar triangles; similar triangles have proportional, not congruent, corresponding sides.

Answer:

A. Corresponding sides of similar triangles are proportional.
C. Corresponding angles of similar triangles are congruent.