Question

8. ABC is a right angled triangle at B. From the mid-point of AC, equal perpendiculars are drawn on AB and BC. Prove that A ABC is an isosceles triangle.​

Answer 1

Step-by-step explanation:

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Let DE and DF be the perpendiculars from D on AB and AC respectively.

In △s BDE and CDF, DE=DF (Given)

∠BED=∠CFD=90

∘

BD=DC (∵ D is the mid-point of BC)

∴ △BDE≅△CDF (RHS)

⇒ ∠B=∠C (cpct)

⇒ AC=AB (Sides opp. equal ∠s are equal)

⇒ △ABC is isosceles.

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Answer 2

Answer:

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