Question

in Fig. 40, point M bisects side BC. ML = MN, ML 1 AB, and MN LAC. Prove that AB = AC.
A
L
N
B
M
C
Fig. 40​

Answer 1

Given : M is the bisector of BC and ML = MN

To prove : AB = AC

Solution :

We will solve this question by using the concept of congruency of triangles.

Two triangles are said to be congruent when they are completely alike to each other.

Consider ∆ LBM and ∆ NCM

∠ MLB = ∠ MNC [ Each 90° ]

ML = MN [ Given ]

BM = CM [ M is bisector of BC ]

So by the property of R.H.S. [ Right angle, Hypotenuse, Side ], ∆ LBM is congruent to ∆ NCM.

So, ∠ B = ∠ C [ By CPCPT ]

AB = AC [ Equal angles have equal opposite sides ]

Hence proved

Learn More :-

In the adjoining figure,△ABC is an isosceles triangle in which AB = AC. If E and F be the midpoints of AC and AB respectively, prove that BE = CF.

https://brainly.in/question/44235531