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 angle ADE is 36°.
Triangle ABC with segment DE. Angle ADE measures 36 degrees.
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