ABC is an isosceles triangle with AB =AC and BD,CE are its two medians. Show that BD=CE .

Explanation

Given `Delta ABC ` is an isosceles triangle in which AB =AC and BD,CE are its two medians.
To show BD=CE

Proof In `Delta ABD and Delta ACE, " "AB=AC " " [Given]`
`" "angleA=angleA " "["Common angle"]`
and AD=AE
`therefore " " AB=AC `
`rArr" "(1)/(2)AB=(1)/(2)AC`
`rArr " "AE=AD`
As D is the mid -Point of AC and E is the mid-Point of AB.
`therefore " "Delta ABD cong Delta ACE " "["by SAS congruence rule"]`
`rArr " "BD=CE " "["by CPCT"]`