ABC is an isosceles triangle with AB = AC and AD ⊥ BC. Is ∆ADB ≅ ∆ACD ?
Question
ABC is an isosceles triangle with AB = AC and AD ⊥ BC. Is ∆ADB ≅ ∆ACD ?
Solution
Yes, triangle ADB is congruent to triangle ACD. Here's why:
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We know that AB = AC because it's given that ABC is an isosceles triangle.
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It's given that AD is perpendicular to BC, which means that ∠ADB = ∠ACD = 90°.
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AD is common to both triangles.
So, by the RHS (Right angle-Hypotenuse-Side) rule of congruency, ∆ADB is congruent to ∆ACD.
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