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 ∠ADE is 68°.
Triangle ABC with segment DE. Angle ADE measures 68 degrees.
The proof, with a missing reason, proves that the measure of ∠ECB is 22°.
Statement Reason
m∠ADE = 68° Given
m∠DAE = 90° Definition of a right angle
m∠AED = 22° 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 = 22° Substitution property
Which of the following can be used to fill in the missing reason?
Triangle Inequality Theorem
Midsegment of a Triangle Theorem
Concurrency of Medians Theorem
Isosceles Triangle Theorem