Question

In a right triangle ABC, CD is the angle bisector of the right angle C. Two lines DF and DE are parallel to the legs of the triangle. Prove that DFCE is a square.

find the following
m∠CED = 180° − m∠ _____ = ___ 

by reason ________ m∠CFD = 180° − m∠ _____ = ___  by reason ________

Answer 1

Please bear with my lengthy answer.

ED || CF - given
∠EDC = ∠DCF - alternate interior angles
m∠CED = 180 - (45+45) = 180 - 90 = 90° - sum of angles in a triangle is 180
∠FDC = ∠ECD - alternate interior angles
m∠CFD = 180 - (45+45) = 180 - 90 = 90° - sum of angles in a triangle is 180
m∠EDF = 360 - (90+90+90) = 360 - 270 = 90° - sum of angles in a quadrilateral is 360