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Mathematics, 29.07.2020 04:01 montgomerykarloxc24x
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°.
StatementReason
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 ACGiven
segment DE is parallel to segment BC?
∠ECB ≅ ∠AEDCorresponding 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
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