##
Problems

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.