Question

in the adjacent figure ABCD is a rectangle if BM and DN are perpendicular from B and D on AC. prove that triangle BMC congruence triangle DNA. is it true that BM=DN?

Answer 1

In triangle BMC and triangle DNA
BC =AD(opposite sides of rectangle are equal)
Angle BCM=Angle MAD(Alternate angles)
Angle BMC =Angle DNA (BM and DN perpendicular to AC)
Therefore triangle BMC congruent to triangle DNA
Therefore BM =DN (cpct)

Answer 2

Pls refer to this :-

In triangle BMC and triangle DNA,

BC = AC (opposite sides are equal)

Angle BCM = angle MAD (alternative angles)

Angle BMC = angle DNA (BM and DN are perpendicular to AC)

So, Triangle BMC is congruent to triangle DNA

Therefore, BM = DN (Cpct)