Question

11. AABC is an isosceles triangle with AB - AC. AM is the bisector of
∆BAC. Prove that ∆ABM ∆ACM
(Hint: Use ASA congruence criterion as BAM - ∆CAM.
AB - AC and ∆ABC = ∆ACM)​

Answer 1

Step-by-step explanation:

We have to draw AP perpendicular to BC. Since △ABC is isosceles, AB=AC.

Given, AM perpendicular to BC

∴∠AMB=∠AMC=90

o

In △ABM and △ACM,

∠AMB=∠AMC=90

o

AM=AC;AM=AM [common]

△ABM≅△ACM [RHS Congruence Rule]

∴∠B=∠C [by CPCT]