Prove the Following:

Question

In the figure, AE = BC and DE = DC. If D lies on the ⊥ bisector of AB, prove that AC = BE

Answer 1

AD = BD .....on perpendicular bisector of AB

Triangle DBC is congruent to triangle DAE .... SSS

Angle DCB=Angle DEA .... corresponding parts of congruent triangles

Angle DEC=Angle DCE ..... base angles of an isosceles triangle

Angle ECB = Angle CEA .... subtraction

Triangle ECB is congruent to triangle CEA .... SAS

AC=BE... corresponding parts of congruent triangles.