Mathematics
Assertion (A): If triangle ABC is isosceles with AC = BC and AB2 = 2AC2, then triangle ABC is right angled.
Reason (R): If in a triangle ABC, we have AB2 = 2AC2 then we can conclude that it is right angled triangle.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Pythagoras Theorem
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Answer
Given, triangle ABC is isosceles with AC = BC and, AB2 = 2AC2
⇒ AB2 = AC2 + AC2
⇒ AB2 = AC2 + BC2
This equation AB2 = AC2 + BC2 is the form of the Pythagorean Theorem where AB is the hypotenuse and AC and BC are the other sides of te triangle.
Since, pythagoras theorem is satisfied, thus ABC is a right angle triangle.
∴ Assertion (A) is true.
Alone with the relation, AB2 = 2AC2, we cannot conclude that it is right angled triangle because there is no mention of the third side BC.
∴ Reason (R) is false.
∴ Assertion (A) is true, Reason (R) is false.
Hence, option 1 is the correct option.
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Related Questions
Consider the following two statements:
Statement 1: The area of a square whose diagonal is 6 cm is 36 cm2.
Statement 2: A diagonal of a square divides it into two right angled isosceles triangle.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
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Reason (R): In a rectangle, all angles are 90°.
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Assertion (A): A triangle with sides 2 cm, 3 cm, 4 cm is not a right angled triangle.
Reason (R): A triangle with sides 2 cm, 3 cm, 4 cm is a scalene triangle.
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In the figure given below, AD ⊥ BC, AB = 25 cm, AC = 17 cm and AD = 15 cm. Find the length of BC.
