Question

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?
A. Concurrency of Medians Theorem
B. Isosceles Triangle Theorem
C. Midsegment of a Triangle Theorem
D. Triangle Inequality Theorem

Answer 1

Answer:

C. Midsegment of a Triangle Theorem

Step-by-step explanation:

After you eliminate the nonsense choices, the answer remains.

A - concurrency of medians requires 2 or more medians. There are no medians in this problem

B - there is no indication the triangle is isosceles

C - the applicable choice (segment DE is a

"midsegment", hence parallel to BC)

D - has to do with measures of sides, which are not involved in this problem

Answer 2

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Answer:

  C. Midsegment of a Triangle Theorem

Step-by-step explanation:

After you eliminate the nonsense choices, the answer remains.

A - concurrency of medians requires 2 or more medians. There are no medians in this problem

B - there is no indication the triangle is isosceles

C - the applicable choice (segment DE is a "midsegment", hence parallel to BC)

D - has to do with measures of sides, which are not involved in this problem