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Two right angled triangles are congruent if :
I.The hypotenuse of one triangle is equal to the hypotenuse of the other.
II.a side for one triangle is equal to the corresponding side of the other.
III.Sides of the triangles are equal.
IV. An angle of the triangle are equal.
Of these statements, the correct ones are combination of:
I.The hypotenuse of one triangle is equal to the hypotenuse of the other.
II.a side for one triangle is equal to the corresponding side of the other.
III.Sides of the triangles are equal.
IV. An angle of the triangle are equal.
Of these statements, the correct ones are combination of:
- a)I and II
- b)II and III
- c)I and III
- d)IV only
- e)I and IV
Correct answer is option 'A'. Can you explain this answer?
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Two right angled triangles are congruent if :I.The hypotenuse of one t...
Two right angled triangle are congruent if the hypotenuse of one triangle is equal to the hypotenuse of the other and a side of one triangle is equal to the corresponding side of the other triangle
Most Upvoted Answer
Two right angled triangles are congruent if :I.The hypotenuse of one t...
Explanation:
To determine which statements are correct for two right-angled triangles to be congruent, let's analyze each statement one by one:
I. The hypotenuse of one triangle is equal to the hypotenuse of the other.
This statement is correct. The hypotenuse is the side opposite the right angle in a right-angled triangle. If the hypotenuse of one triangle is equal to the hypotenuse of another triangle, then the triangles are congruent by the Hypotenuse-Leg Congruence Theorem.
II. A side for one triangle is equal to the corresponding side of the other.
This statement is correct. If a side of one triangle is equal to the corresponding side of another triangle, then the triangles are congruent by the Side-Side-Side (SSS) Congruence Theorem.
III. Sides of the triangles are equal.
This statement is incorrect. While it is true that if all three sides of one triangle are equal to the corresponding sides of another triangle, then the triangles are congruent, this statement does not specify which sides are equal. It is possible for two triangles to have equal sides but still not be congruent because the angles may be different.
IV. An angle of the triangle is equal.
This statement is incorrect. While it is true that if all three angles of one triangle are equal to the corresponding angles of another triangle, then the triangles are congruent, this statement only mentions that "an angle" is equal. It does not specify which angle is equal, and therefore, it cannot be used to determine congruence.
Conclusion:
The correct statements for two right-angled triangles to be congruent are I. The hypotenuse of one triangle is equal to the hypotenuse of the other and II. A side for one triangle is equal to the corresponding side of the other. Therefore, the correct answer is option 'A': I and II.
To determine which statements are correct for two right-angled triangles to be congruent, let's analyze each statement one by one:
I. The hypotenuse of one triangle is equal to the hypotenuse of the other.
This statement is correct. The hypotenuse is the side opposite the right angle in a right-angled triangle. If the hypotenuse of one triangle is equal to the hypotenuse of another triangle, then the triangles are congruent by the Hypotenuse-Leg Congruence Theorem.
II. A side for one triangle is equal to the corresponding side of the other.
This statement is correct. If a side of one triangle is equal to the corresponding side of another triangle, then the triangles are congruent by the Side-Side-Side (SSS) Congruence Theorem.
III. Sides of the triangles are equal.
This statement is incorrect. While it is true that if all three sides of one triangle are equal to the corresponding sides of another triangle, then the triangles are congruent, this statement does not specify which sides are equal. It is possible for two triangles to have equal sides but still not be congruent because the angles may be different.
IV. An angle of the triangle is equal.
This statement is incorrect. While it is true that if all three angles of one triangle are equal to the corresponding angles of another triangle, then the triangles are congruent, this statement only mentions that "an angle" is equal. It does not specify which angle is equal, and therefore, it cannot be used to determine congruence.
Conclusion:
The correct statements for two right-angled triangles to be congruent are I. The hypotenuse of one triangle is equal to the hypotenuse of the other and II. A side for one triangle is equal to the corresponding side of the other. Therefore, the correct answer is option 'A': I and II.
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Two right angled triangles are congruent if :I.The hypotenuse of one triangle is equal to the hypotenuse of the other.II.a side for one triangle is equal to the corresponding side of the other.III.Sides of the triangles are equal.IV.An angle of the triangle are equal.Of these statements, the correct ones are combination of:a)I and IIb)II and IIIc)I and IIId)IV onlye)I and IVCorrect answer is option 'A'. Can you explain this answer?
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Two right angled triangles are congruent if :I.The hypotenuse of one triangle is equal to the hypotenuse of the other.II.a side for one triangle is equal to the corresponding side of the other.III.Sides of the triangles are equal.IV.An angle of the triangle are equal.Of these statements, the correct ones are combination of:a)I and IIb)II and IIIc)I and IIId)IV onlye)I and IVCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Two right angled triangles are congruent if :I.The hypotenuse of one triangle is equal to the hypotenuse of the other.II.a side for one triangle is equal to the corresponding side of the other.III.Sides of the triangles are equal.IV.An angle of the triangle are equal.Of these statements, the correct ones are combination of:a)I and IIb)II and IIIc)I and IIId)IV onlye)I and IVCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two right angled triangles are congruent if :I.The hypotenuse of one triangle is equal to the hypotenuse of the other.II.a side for one triangle is equal to the corresponding side of the other.III.Sides of the triangles are equal.IV.An angle of the triangle are equal.Of these statements, the correct ones are combination of:a)I and IIb)II and IIIc)I and IIId)IV onlye)I and IVCorrect answer is option 'A'. Can you explain this answer?.
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Solutions for Two right angled triangles are congruent if :I.The hypotenuse of one triangle is equal to the hypotenuse of the other.II.a side for one triangle is equal to the corresponding side of the other.III.Sides of the triangles are equal.IV.An angle of the triangle are equal.Of these statements, the correct ones are combination of:a)I and IIb)II and IIIc)I and IIId)IV onlye)I and IVCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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