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In the diagram, ABD and BCD are isosceles triangles, where AB = BC= BD. The special name that is given to quadrilateral ABCD is:(a) rectangle (b) kite (c) parallelogram (d) trapezium |
Answer» (d) trapezium In Δ BAD, ∠ BDA=∠BAD= 57° (isos. Δ property) In Δ BDC, ∠BCD=∠BDC= 66° (isos. Δ property) ∴ ∠D = 57° + 66° = 123° and ∠A +∠D = 57° + 123° = 180° Also, ∠D + C = 123° + 66° = 189° Hence, by the property that co-int. angles are supplementary ⇒ lines are parallel, we have AB || DC and AD not || BC. Hence ABCD is a trapezium. |
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