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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 angles 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 angles 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
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 ...
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.
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Two right angled triangles are congruent if :I. The hypotenuse of one ...
Explanation:
To determine the correct combinations of statements that make two right-angled triangles 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 true. According to the Hypotenuse-Leg (HL) congruence criterion, if the hypotenuse and one leg of a right-angled triangle are congruent to the hypotenuse and one leg of another right-angled triangle, then the two triangles are congruent.
II. A side for one triangle is equal to the corresponding side of the other.
- This statement is also true. According to the Side-Angle-Side (SAS) congruence criterion, if a side, an angle, and another side of one triangle are congruent to the corresponding side, angle, and side of another triangle, then the two triangles are congruent.
III. Sides of the triangles are equal.
- This statement is not always true. Two right-angled triangles can have equal sides, but it does not guarantee congruence. For example, consider two right-angled triangles with sides 3, 4, 5 and 6, 8, 10. Both triangles have equal sides, but they are not congruent as they have different angles.
IV. Angles of the triangle are equal.
- This statement is also not always true. Two right-angled triangles can have equal angles, but it does not guarantee congruence. For example, consider two right-angled triangles with angles 30°, 60°, 90° and 45°, 45°, 90°. Both triangles have equal angles, but they are not congruent as they have different side lengths.
Therefore, the correct combination of statements that make two right-angled triangles congruent is I and II. The hypotenuse and one side of one triangle must be equal to the hypotenuse and corresponding side of the other triangle for them to be congruent.
To determine the correct combinations of statements that make two right-angled triangles 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 true. According to the Hypotenuse-Leg (HL) congruence criterion, if the hypotenuse and one leg of a right-angled triangle are congruent to the hypotenuse and one leg of another right-angled triangle, then the two triangles are congruent.
II. A side for one triangle is equal to the corresponding side of the other.
- This statement is also true. According to the Side-Angle-Side (SAS) congruence criterion, if a side, an angle, and another side of one triangle are congruent to the corresponding side, angle, and side of another triangle, then the two triangles are congruent.
III. Sides of the triangles are equal.
- This statement is not always true. Two right-angled triangles can have equal sides, but it does not guarantee congruence. For example, consider two right-angled triangles with sides 3, 4, 5 and 6, 8, 10. Both triangles have equal sides, but they are not congruent as they have different angles.
IV. Angles of the triangle are equal.
- This statement is also not always true. Two right-angled triangles can have equal angles, but it does not guarantee congruence. For example, consider two right-angled triangles with angles 30°, 60°, 90° and 45°, 45°, 90°. Both triangles have equal angles, but they are not congruent as they have different side lengths.
Therefore, the correct combination of statements that make two right-angled triangles congruent is I and II. The hypotenuse and one side of one triangle must be equal to the hypotenuse and corresponding side of the other triangle for them to be congruent.
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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 angles 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 onlyCorrect answer is option 'A'. Can you explain this answer?
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