Question

In triangleABC,angle A=angle C and BM bisects angle ABC. PROVE that BM is perpendicular to AC​

Answer 1

Step-by-step explanation:

in triangle abc angle a is equal to angle c

ab=bc (angles opposite to equal angles are equal)---------1

in triangle amb and in triangle cmb

angle c = angle a(given)

bm=bm(common)

ab=bc (by 1)

by sas criteria triangle amb is congruent to triangle cmb

so angle bcm=amb

but

angle bcm+angle amb=180 (linear pair)

2anglebcm=180 (angle bcm=amb)

angle bcm =90

so angle amb=90 (angle bcm= angle amb)

so bm is perpendicular to achieve

I hope you got it.