It is given that 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 47°.
To prove: The measure of angle ECB is 43°.
1. m∠ADE=47° Given
2. m∠DAE=90° definition of right angle
3. In ΔADE, ∠ADE+∠DAE+∠DEA=180°
⇒∠DEA=43° triangle sum theorem
4. ∠ECB=43° substitution property
5.Segment DE joins the midpoints
of segment AB and AC Given
6. Segment DE is parallel to segment BC Midsegment theorem
7. m∠ECB≅m∠AED Corresponding angles are congruent
therefore, Measure of angle AED is 43°.
Hence, option A is correct.