Question

Abcd is a rhombus eabf is a straight line such that ea=ab=bf probe that

Answer 1

We know that the diagonals of a rhombus are perpendicular bisector of each other In ΔBDE A O , and are mid points of BE and BD respectively In ΔCFA B O , and are mid points of AF and AC respectively

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Answer 2

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SinceΔEAD=ΔABC

(Corresponding angles),&AD=BC(sides of the rhombus)

By side angle side congrugency,the triangles

Therefore the corresponding parts of the triangle are also equal.

ΔCBF & ΔDAB

Since the sides 

BF=AB

∠CBF∠DAB(corresponding angles)

ΔCBF&ΔDAB are congrugent

ΔAOB

∠ABO+∠BAO+∠AOB=180°

∠ABO+∠BAO=90°

∠CFB+∠AED=90°

∠XFE+∠XEF=90°

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