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Question

$△ E A C ≅△ B A F$ .

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Solution

Verified by Toppr

Given ABDE and AFGC are squares and ABC is a right triangle.
To prove: triangle EAC congruent to triangle BAF
Proof:
Consider triangles EAC and BAF:
1) EA = AB [EA and AB are sides of the square ABDE]
2) AC = AF [AC and AF are sides of the square AFGC]
3) $∠ E A C = ∠ E A B + ∠ B A C ∠ B A F = ∠ B A C + ∠ C A F [∠ E A B = ∠ C A F = 90 d e g] ⟹ ∠ E A C = ∠ B A F$
Hence the triangles EAC and BAF are congruent by SAS rule.

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