Prove the Following:

Question

Given: E is the midpoint of segment AB , segment AD ⊥ segment AB , segment BC ⊥ segment AB, ∠ADE ≅ ∠BCE

Prove: Angle EDC is congruent to angle ECD

Answer 1

triangle ADE and triangle BCE are both right triangles.....definition of perpendicular

length of AE = length of EB.....given

m angle ADE = m angle BCE.....given

triangle ADE is congruent to triangle BCE.....right triangle with leg and angle equal

length of DE = length of EC.....corresponding arts of congruent triangles

m angle EDC=m angle ECD.....base angles of an isosceles triangle