If AD is an altitude of an isosceles tri

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

If AD is an altitude of an isosceles triangle ABC in which AB = AC. Then:

Options:

BD=CD

BD>CD

BD<CD

None of the above

Correct Answer:

BD=CD

Explanation:

In ΔABD and ΔACD,
∠ADB = ∠ADC = 90°
AB = AC (Given)
AD = AD (Common)
∴ ΔABD ≅ ΔACD (By RHS congruence condition)
BD = CD

We can also use AAS criteria as ∠ABD and ∠ACD are equal (Sides AB and AC are equal)