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In an isosceles triangle ABC, if AC = BC and AB 2 = 2AC 2 , then the measure of angle C will be

(a) 30°   (b) 45°   (c) 60°   (d) 90°

 

This question is inspired from Ex 6.5, 5 - Chapter 6 Class 10 - Triangles

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Question 16 In an isosceles triangle ABC, if AC = BC and AB2 = 2AC2 , then the measure of angle C will be (a) 30° (b) 45° (c) 60° (d) 90° Given AB2 = 2AC2 AB2 = AC2 + AC2 Putting AC = BC AB2 = AC2 + BC2 Since this converse of Pythagoras theorem It means Δ ABC is right angled triangle With Hypotenuse AB Since right angle is opposite to hypotenuse ∴ ∠ C = 90° So, the correct answer is (d)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.