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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

A square is inscribed in an isosceles right angle so that the square and the triangle have one angle common show that the vertices of the square opposite

Given: ABC is a triangle right angled at B and AB=BC DEFB is square To prove: AE=EC Proof: Since DEFB is a square BD=BF⇒eq.1 and.... AB=BC(given)⇒eq.2 By subtracting eq.2 with eq.1, we get AB-BD=BC-BF AD=FD⇒eq.3

In ΔADE and ΔEFC ∠EAD=∠ECF (∵ AB=AC) AF=FC (from eq.3) ∠ADE=∠EFC (adjoining angles of the square) ∴ By ASA congruency rule ΔEDA is congruent to ΔEFC by cpct AE=EC Hence proved