Write a direct proof for the following problems.
Problem :
Given:
Circle C with triangles ABC and DEC.
Chord AB is congruent to chord DE.
Prove:
Triangles ABC and DEC are congruent.
Problem :
Given:
Qaudrilateral DEFG is a parallelogram.
Prove:
Angles G and E are congruent
Do not use any previously learned theorems. Use the definition of a
parallelogram.
Problem :
Given:
Segment BD is a median of triangle ABC.
Segment DE is a median of triangle ADB.
Segment DE is perpendicular to segment AB.
Prove:
Triangle DBC is isosceles.