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CBSE Class 9 Mathematics Question 18 of 21

Triangles — Question 2

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Question

Question 2

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that

(i) AD bisects BC

(ii) AD bisects ∠A

Answer

Given :

Δ ABC is an isosceles triangle and AB = AC.

AD is altitude

∴ ∠ADB = ∠ADC = 90°.

AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that. NCERT Class 9 Mathematics CBSE Solutions.

(i) In Δ BAD and Δ CAD,

⇒ ∠ADB = ∠ADC (Each equal to 90° as AD is altitude)

⇒ AB = AC (Given)

⇒ AD = AD (Common)

∴ Δ BAD ≅ Δ CAD (By R.H.S. Congruence rule)

We know that,

Corresponding parts of congruent triangles are equal.

∴ BD = CD (By C.P.C.T.)

Hence, proved that AD bisects BC.

(ii) Since, Δ BAD ≅ Δ CAD

∴ ∠BAD = ∠CAD (By C.P.C.T.)

Hence, proved that AD bisects ∠A.