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Question 1
ABC is an isosceles triangle with AB = AC and BD, CE are its two medians. Show that BD = CE.

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Solution

ΔABC is an isosceles triangle in which AB=AC and BD,CE are its two medians.

In ΔABC and ΔACE,
AB = AC [given]
A=A [common angle]
And AD = AE
[AB=AC12AB=12ACAE=AD]
As D is the mid-point of AC and E is the mid-point of AB,
ΔABCΔACE [by SAS congruence rule]
BD=CE [by CPCT]


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