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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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.
Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then the
ratio of their areas is 6/5.
- 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 'C'. Can you explain this answer?
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Direction: In the following questions, A statement of Assertion (A) i...
In case of assertion: In the given two right triangles, both have equal right angles and one of the acute angles of one triangle is equal to an acute angle of the other triangle.
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Thus, by AA similarity, the given two triangles are similar.
∴ Assertion is correct.
In case of reason:
We know that the ratio of the areas of two similar triangles is the square of the ratio of the corresponding altitudes of two similar triangles.
Thus, the ratio of the areas of two similar triangles is (3/5)2 = 9/25.
Most Upvoted Answer
Direction: In the following questions, A statement of Assertion (A) i...
Assertion (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then the triangles will be similar.
Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then the ratio of their areas is 6/5.
Explanation:
Similar triangles have corresponding angles that are equal and corresponding sides that are proportional. In this case, we are given that one of the acute angles of one right triangle is equal to an acute angle of the other right triangle.
To prove that the triangles are similar, we need to show that their corresponding angles are equal. Since one of the acute angles of one triangle is equal to an acute angle of the other triangle, we can say that the two triangles have at least one pair of equal angles.
Now, let's understand the reason given in the statement. The reason states that if the ratio of the corresponding altitudes of two similar triangles is 3/5, then the ratio of their areas is 6/5.
Proof of Reason (R):
Let's consider two similar triangles, Triangle ABC and Triangle XYZ, where Triangle ABC is the larger triangle and Triangle XYZ is the smaller triangle.
Let h1 and h2 be the altitudes of Triangle ABC and Triangle XYZ respectively.
Since the triangles are similar, the ratio of their corresponding altitudes is given as h1/h2 = 3/5.
Now, let's find the ratio of their areas.
The area of a triangle is given by the formula: Area = (1/2) * base * height.
Let's assume the base of Triangle ABC is b1 and the base of Triangle XYZ is b2.
The area of Triangle ABC is given by (1/2) * b1 * h1.
The area of Triangle XYZ is given by (1/2) * b2 * h2.
To find the ratio of their areas, we can write:
Area of Triangle ABC / Area of Triangle XYZ = [(1/2) * b1 * h1] / [(1/2) * b2 * h2]
Canceling out the common factors, we get:
Area of Triangle ABC / Area of Triangle XYZ = (b1 * h1) / (b2 * h2)
Now, substituting the given ratio of altitudes, we have:
Area of Triangle ABC / Area of Triangle XYZ = (b1 * h1) / (b2 * h2) = (b1 * (3/5)) / (b2 * 1) = (3/5) * (b1/b2)
Therefore, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding altitudes.
In this case, the ratio of the areas is (3/5)^2 = (9/25) = 9/25.
Hence, the given reason is incorrect.
Therefore, the correct answer is option 'C' - A is true but R is false.
Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then the ratio of their areas is 6/5.
Explanation:
Similar triangles have corresponding angles that are equal and corresponding sides that are proportional. In this case, we are given that one of the acute angles of one right triangle is equal to an acute angle of the other right triangle.
To prove that the triangles are similar, we need to show that their corresponding angles are equal. Since one of the acute angles of one triangle is equal to an acute angle of the other triangle, we can say that the two triangles have at least one pair of equal angles.
Now, let's understand the reason given in the statement. The reason states that if the ratio of the corresponding altitudes of two similar triangles is 3/5, then the ratio of their areas is 6/5.
Proof of Reason (R):
Let's consider two similar triangles, Triangle ABC and Triangle XYZ, where Triangle ABC is the larger triangle and Triangle XYZ is the smaller triangle.
Let h1 and h2 be the altitudes of Triangle ABC and Triangle XYZ respectively.
Since the triangles are similar, the ratio of their corresponding altitudes is given as h1/h2 = 3/5.
Now, let's find the ratio of their areas.
The area of a triangle is given by the formula: Area = (1/2) * base * height.
Let's assume the base of Triangle ABC is b1 and the base of Triangle XYZ is b2.
The area of Triangle ABC is given by (1/2) * b1 * h1.
The area of Triangle XYZ is given by (1/2) * b2 * h2.
To find the ratio of their areas, we can write:
Area of Triangle ABC / Area of Triangle XYZ = [(1/2) * b1 * h1] / [(1/2) * b2 * h2]
Canceling out the common factors, we get:
Area of Triangle ABC / Area of Triangle XYZ = (b1 * h1) / (b2 * h2)
Now, substituting the given ratio of altitudes, we have:
Area of Triangle ABC / Area of Triangle XYZ = (b1 * h1) / (b2 * h2) = (b1 * (3/5)) / (b2 * 1) = (3/5) * (b1/b2)
Therefore, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding altitudes.
In this case, the ratio of the areas is (3/5)^2 = (9/25) = 9/25.
Hence, the given reason is incorrect.
Therefore, the correct answer is option 'C' - A is true but R is false.
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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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. Can you explain this answer?
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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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. Can you explain this answer? for Class 10 2024 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. Can you explain this answer? for Class 10 2024 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. 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 (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then theratio of their areas is 6/5.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 'C'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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