Question

16. In the given figure, ABCD is a rectangle.,
BM and DN are perpendiculars from B and D on AC. Prove that. (a) TriangleBMC congruence Triangle DNA. (b) BM=DN​

Answer 1

Answer:

GivenABCD is a quadrilateral in which diagonals AC and BD intersect each other at P

Also,DN⊥AC and BM⊥AC

DN=BM

In △DNP and △BMP we have

∠DAN=∠BCM since they are vertically opposite angles.

∠DNA=∠BMC since each are equal to 90∘

BC = DA (Opposite sides of rectangle are equal)

⇒△DNA≅△BMC by AAS postulate.

⇒BM = DN by C.P.C.T

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