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Question

In the diagram, ABD and BCD are isosceles triangles, where AB=BC=BD. What type of a quadrilateral is ABCD?

A
Rectangle
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B
Kite
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C
Parallelogram
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D
Trapezium
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Solution

The correct option is D Trapezium
In, ΔBAD
BDA=BAD=57 [equal sides subtend equal angles]
In ΔBDC,
BCD=BDC=66 [equal sides subtend equal angles]
D=57+66=123
A+D=57+123=180
Also, D+C=123+66=189
Hence, by the property that co-interior angles are supplementary, line ABDC,.
However, AD not parallel to BC.
Hence, ABCD is a trapezium.

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