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Question

ABCD is a quadrilateral in which ¯¯¯¯¯¯¯¯AB=¯¯¯¯¯¯¯¯¯AD and ¯¯¯¯¯¯¯¯BC=¯¯¯¯¯¯¯¯¯DC. Diagonals ¯¯¯¯¯¯¯¯AC and ¯¯¯¯¯¯¯¯¯BD intersect each other at O.

A
ΔABCΔADC
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B
ΔAOBΔAOD
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C
¯¯¯¯¯¯¯¯AC¯¯¯¯¯¯¯¯¯BD
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D
¯¯¯¯¯¯¯¯AC bisects ¯¯¯¯¯¯¯¯¯BD
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Solution

The correct options are
B ΔAOBΔAOD
C ¯¯¯¯¯¯¯¯AC¯¯¯¯¯¯¯¯¯BD
D ¯¯¯¯¯¯¯¯AC bisects ¯¯¯¯¯¯¯¯¯BD
AB=AD(Given)

BC=DC(Given)

AC=AC(common)

Therefore triangle ABC congruent ACD[SSS]

BOA=AOD=90o

AB=AD(Given)

AO=AO(common)

BOA=AOD=90o

ΔAOBΔAOD

ACBD(ABCD is a quadrilateral)

AC bisects BD.

(one diagonal of a quadrilateral bisect the other)

Hence, correct option is B, C, D.

1224182_1451913_ans_7e88e807ea894b6c85f2aa3ac0f72d37.png

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