Question

In quadrilateral ABCD, B is reflection of D in AC and AE bisects angle CAD such that C is on CD,Angle DEA is 3 times angle DAE, PROVE BCD is a rhombus

Answer 1

Answer:

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Step-by-step explanation:

AC and BD are diagonals . So let they intersect at O.

In triangles ABC and ADC,

angle CAB = angle CAD

angle ACB = angle ACD

AC = AC

Therefore, triangles ABC and ADC are congruent.

NOW,

AB = AD (corresponding parts of congruent triangles)

In triangle ABD,

AB = AD

So, triangle ABD is isosceles.

As we know the angle bisector of the vertical angle of an isosceles triangle

is also the perpendicular bisector of the base.

So AC intersects BD at right angle.

so angle AOD = 90o.