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CBSE Class 9 Mathematics Question 21 of 21

Triangles — Question 5

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Question 5

ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C.

Answer

Given :

Δ ABC is an isosceles with AB = AC.

Draw AP ⊥ BC,

∴ ∠APB = ∠APC = 90°

ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C. NCERT Class 9 Mathematics CBSE Solutions.

In Δ APB and Δ APC,

⇒ ∠APB = ∠APC (Each equal to 90°)

⇒ AB = AC (Since ABC is an isosceles triangle)

⇒ AP = AP (Common)

∴ Δ APB ≅ Δ APC (By R.H.S. congruence rule)

We know that,

Corresponding parts of congruent triangle are equal.

∴ ∠B = ∠C (By C.P.C.T.)

Hence, proved that ∠B = ∠C.