Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angl
e ADE is 36°. 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 segment DE joins the midpoints of segment AB and segment AC Given segment DE is parallel to segment 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
Midsegment of a Triangle Theorem - is the right choice
<em>The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.</em>
