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CBSE Class 9 Mathematics Question 10 of 21

Triangles — Question 2

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Question 2

In Δ ABC, AD is the perpendicular bisector of BC. Show that Δ ABC is an isosceles triangle in which AB = AC.

In Δ ABC, AD is the perpendicular bisector of BC. Show that Δ ABC is an isosceles triangle in which AB = AC. NCERT Class 9 Mathematics CBSE Solutions.
Answer

Given :

AD is the perpendicular bisector of BC.

∴ ∠ADB = ∠ADC = 90° and BD = DC.

In Δ ADC and Δ ADB,

⇒ AD = AD (Common side)

⇒ ∠ADC = ∠ADB (Each equal to 90°)

⇒ CD = BD (AD is the perpendicular bisector of BC)

∴ Δ ADC ≅ Δ ADB (By S.A.S. congruence rule)

We know that,

Corresponding parts of congruent triangles are equal.

∴ AB = AC (By C.P.C.T.)

Hence, proved that ABC is an isosceles triangle in which AB = AC.