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 ∠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°.StatementReasonm∠ADE = 68°Givenm∠DAE = 90°Definition of a right anglem∠AED = 22°Triangle Sum Theoremsegment DE joins the midpoints of segment AB and segment ACGivensegment DE is parallel to segment BC?∠ECB ≅ ∠AEDCorresponding angles are congruentm∠ECB = 22°Substitution propertyWhich 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

Answer 1

Given:

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.

Required:

To prove that the measure of ∠ECB is 22°.

Explanation:

The triangle ADE is the right triangle.

We know that the sum of all angles of the triangles is 180 degrees.

$\begin{gathered} \angle AED+90\degree+68\degree=180\degree \\ \angle AED+158\degree=180\degree \\ \angle AED=180\degree-158\degree \\ \angle AED=22\degree \end{gathered}$$\begin{gathered} \angle AED=\angle ECB\text{ \lparen Corresponding angles\rparen} \\ \angle ECB=22\degree \end{gathered}$

Final Answer: