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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 triangle right angled at C then AB2 = 2AC2.
Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
- 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 'B'. Can you explain this answer?
Verified Answer
Direction: In the following questions, A statement of Assertion (A) i...
We know that If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This is converse of Pythagoras theorem.
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So, Reason is correct By
Pythagoras theorem, we have AB2 = AC2 + BC2
= AC2 + AC2 [∵ AC = BC Given]
⇒ AB2 = 2AC2So, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A).
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion: ABC is an isosceles triangle right angled at C, then AB^2 = 2AC^2.
Reason: If in a triangle, the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
Explanation:
To prove the given statement, we need to use the Pythagorean theorem and the properties of an isosceles triangle.
Properties of an isosceles triangle:
- An isosceles triangle has two sides of equal length.
- The angles opposite to the two equal sides are also equal.
Proof:
Let's consider the given triangle ABC, where AB is equal to AC.
Using the Pythagorean theorem, we know that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
According to the Pythagorean theorem, in triangle ABC:
AC^2 + BC^2 = AB^2 ...(1)
Since triangle ABC is an isosceles triangle, AC = BC.
Let's substitute AC with BC in equation (1):
BC^2 + BC^2 = AB^2
2BC^2 = AB^2
Since AC = BC, we can rewrite the equation as:
2AC^2 = AB^2
Hence, we can conclude that if triangle ABC is an isosceles triangle right angled at C, then AB^2 = 2AC^2.
Justification of the Reason:
The reason provided is correct. It states that if in a triangle, the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This is a well-known property of right-angled triangles, known as the Pythagorean theorem.
In the given triangle ABC, if AB^2 = 2AC^2, it implies that the square of the hypotenuse (AB) is equal to the sum of the squares of the other two sides (AC^2 + AC^2), which satisfies the condition for a right-angled triangle.
Hence, both the assertion and the reason are true, and the reason correctly explains the assertion.
Therefore, the correct answer is option B.
Reason: If in a triangle, the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
Explanation:
To prove the given statement, we need to use the Pythagorean theorem and the properties of an isosceles triangle.
Properties of an isosceles triangle:
- An isosceles triangle has two sides of equal length.
- The angles opposite to the two equal sides are also equal.
Proof:
Let's consider the given triangle ABC, where AB is equal to AC.
Using the Pythagorean theorem, we know that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
According to the Pythagorean theorem, in triangle ABC:
AC^2 + BC^2 = AB^2 ...(1)
Since triangle ABC is an isosceles triangle, AC = BC.
Let's substitute AC with BC in equation (1):
BC^2 + BC^2 = AB^2
2BC^2 = AB^2
Since AC = BC, we can rewrite the equation as:
2AC^2 = AB^2
Hence, we can conclude that if triangle ABC is an isosceles triangle right angled at C, then AB^2 = 2AC^2.
Justification of the Reason:
The reason provided is correct. It states that if in a triangle, the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This is a well-known property of right-angled triangles, known as the Pythagorean theorem.
In the given triangle ABC, if AB^2 = 2AC^2, it implies that the square of the hypotenuse (AB) is equal to the sum of the squares of the other two sides (AC^2 + AC^2), which satisfies the condition for a right-angled triangle.
Hence, both the assertion and the reason are true, and the reason correctly explains the assertion.
Therefore, the correct answer is option B.
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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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Here you can find the meaning 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. 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 triangle right angled at C then AB2 = 2AC2.Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.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 'B'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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