Question

triangle abc is a right triangle. point d is the mid - point of side ab and point e is the mid - point of side ac. the proof, with a missing reason, proves that the measure of angle ecb is 54°. statement reason m∠ade = 36° given m∠dae = 90° definition of a right angle m∠aed = 54° triangle sum theorem de joins the midpoints of ab and ac given de is parallel to bc? ∠ecb≅∠aed corresponding angles are congruent m∠ecb = 54° substitution property which theorem can be used to fill in the missing reason? concurrency of medians theorem isosceles triangle theorem midsegment of a triangle theorem triangle inequality theorem

Explanation:

The Midsegment of a Triangle Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third - side. Here, since $\overline{DE}$ joins the midpoints of $\overline{AB}$ and $\overline{AC}$, by this theorem, $\overline{DE}$ is parallel to $\overline{BC}$.

Answer:

C. Midsegment of a Triangle Theorem