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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2
Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Direction: In the following questions, A statement of Assertion (A) i...
If Assertion is incorrect, but Reason is correct.
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In right angled ΔABC ,
AB2 = AC2 + BC2(By Pythagoras Theorem)
= AC2 + AC2 [BC = AC]
= 2AC2AB2 = 2AC2
Assertion is false.
Again since, AB2 = 2AC2
= AC2 + AC2 = AC2 + BC2 (AC = BC given)
∠ = 90°
(By converse of Pythagoras Theorem)Reason is true.
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
In isosceles triangle, if right angled at C then
AB
not 2
= 2AC2
AB
2
= 3AC2
therefore assertion is incorrect.
And if
AB
in isosceles triangle, then it means that triangle follows Pythagoras theorem. Consequently, triangle ABC is a right angled triangle in which angle C = 90 degree2
= 2AC2
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Community Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion: ABC is an isosceles, right triangle, right angled at C.
Reason: In an isosceles triangle ABC if AC = BC and AB2 = 2AC2, then ∠C = 90°.
Explanation:
An isosceles triangle is a triangle in which two sides are equal in length. In triangle ABC, AC = BC, which makes it an isosceles triangle.
In an isosceles triangle, the angles opposite to the equal sides are also equal. Therefore, angle ACB = angle ABC.
Since ABC is a right triangle, one of its angles is 90°. Let's assume that angle ACB is the right angle.
Now, let's consider the reason provided in the statement.
If AB2 = 2AC2, then it means that the square of the length of the hypotenuse (AB) is equal to twice the square of the length of one of the legs (AC).
Let's assume that AC = x. Then, AB2 = 2x2.
Taking the square root of both sides, we get AB = √(2x2) = √(4x2) = 2x.
Since ABC is an isosceles triangle, AC = BC, which is equal to x.
Therefore, AB = 2x = 2AC.
From the given reason, AB2 = 2AC2.
Substituting the values, (2AC)2 = 2AC2, which simplifies to 4AC2 = 2AC2.
Dividing both sides by 2AC2, we get 4/2 = 2.
This implies that 2 = 1, which is not true.
Hence, the reason provided is false.
Therefore, the correct answer is option 'D' - A is false and R is True.
Reason: In an isosceles triangle ABC if AC = BC and AB2 = 2AC2, then ∠C = 90°.
Explanation:
An isosceles triangle is a triangle in which two sides are equal in length. In triangle ABC, AC = BC, which makes it an isosceles triangle.
In an isosceles triangle, the angles opposite to the equal sides are also equal. Therefore, angle ACB = angle ABC.
Since ABC is a right triangle, one of its angles is 90°. Let's assume that angle ACB is the right angle.
Now, let's consider the reason provided in the statement.
If AB2 = 2AC2, then it means that the square of the length of the hypotenuse (AB) is equal to twice the square of the length of one of the legs (AC).
Let's assume that AC = x. Then, AB2 = 2x2.
Taking the square root of both sides, we get AB = √(2x2) = √(4x2) = 2x.
Since ABC is an isosceles triangle, AC = BC, which is equal to x.
Therefore, AB = 2x = 2AC.
From the given reason, AB2 = 2AC2.
Substituting the values, (2AC)2 = 2AC2, which simplifies to 4AC2 = 2AC2.
Dividing both sides by 2AC2, we get 4/2 = 2.
This implies that 2 = 1, which is not true.
Hence, the reason provided is false.
Therefore, the correct answer is option 'D' - A is false and R is True.
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB2 = 3AC2Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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