7.3 Properties of Isosceles Triangles

Key Formulas

Solved Examples

Step 1

Given $AB = AC$ . Since E and F are midpoints, $AE = EB = \frac{1}{2}AB$ and $AF = FC = \frac{1}{2}AC$ . Thus $AB=AC \implies AE=AF$ .

Step 2

Consider $\Delta ABF$ and $\Delta ACE$ .

Step 3

$AB = AC$ (Given).

Step 4

$\angle A = \angle A$ (Common).

Step 5

$AF = AE$ (Halves of equal sides).

Step 6

By SAS, $\Delta ABF \cong \Delta ACE$ .

Step 7

Therefore, $BF = CE$ (CPCT).

Final Answer

Proved.

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