Question

In the adjoining figure, ∆ABC is an isosceles triangle with AB=AC in which E is the midpoint of AC

and F is the midpoint of AB. Show that ∆BCF≅ ∆CBE and BE=CF​

Answer 1

Step-by-step explanation:

AB=AC (given-isoceles)

AB/2=AC/2

FB=EC ----(1)

in ∆BCF and ∆CBE

FB=EC (1) [side]

angle FBC=angle ECB (angles adjacent to the equal sides of and isoceles triangle are equal) [angle]

BC=BC (common side) [side]

therefore, ∆BCF≅ ∆CBE by SAS congruency rule

BE=CF by CPCT

CPCT - corresponding parts of congruent triangles.