Question

Question 43

In the given figure, M is the mid-point of both AC and BD. Then,

a) $\angle 1=\angle 2$
b) $\angle 1=\angle 4$
c) $\angle 2=\angle 4$
d) $\angle 1=\angle 3$

Answer 1

In $\Delta AMB$ and $\Delta CMD$, AM = CM [M is the mid-point]
BM = DM [M is the mid-point]
$\angle AMB=\angle CMD$ [vertically opposite angles]
By SAS congruence criterion,
$\Delta AMB\cong \Delta CMD$
$\therefore \angle 1=\angle 4$ [by CPCT]