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Question

Which of the following statements are true?


Correct Answer
A
ABD  BCD
Your Answer
B
BMC  CMD
Correct Answer
C
AMB  CMD
Your Answer
D
AMB  BMC

Solution

The correct options are
A ABD  BCD
C AMB  CMD
1. ABD  BCD
AB = CD (Opposite sides of a parallelogram)
AD = BC (Opposite sides of a parallelogram)
BD = BD (Common side)
Triangles are congruent by SSS congruence criterion.

2. BMC  CMD
The triangles are not congruent by SSS / SAS / ASA / RHS congruence criterion.

3. AMB  CMD
AM = MC ( Diagonals of a parellogram bisect each other)
BM = MD ( Diagonals of a parellogram bisect each other)
AMD = CMD ( Vertically opposite angles)
By SAS congruence criterion, the triangles are congruent.

4. AMB  BMC
The triangles are not congruent by SSS / SAS / ASA / RHS congruence criterion.

Hence, options ABD  BCD  and  AMB  CMD are correct.

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