Mathematics
In the adjoining figure, AB = AC and AD is median of △ABC, then ∠ADC is equal to
60°
120°
90°
75°
Triangles
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Answer
In △ADB and △ADC,
Given,
AB = AC (Given)
BD = DC (Given)
AD = AD (Common)
Hence, △ADB ≅ △ADC by SSS axiom.
We know that corresponding parts of congruent triangle are equal.
∴ ∠ADB = ∠ADC = x.
From figure,
⇒ ∠ADB + ∠ADC = 180°
⇒ x + x = 180°
⇒ 2x = 180°
⇒ x = 90°
∴ ∠ADC = 90°.
Hence, Option 3 is the correct option.
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