Class 9 Exam > Class 9 Questions > Choose the correct statementa)Two right trian...
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Choose the correct statement
- a)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangle
- b)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles
- c)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruent
- d)Sides opposite equal angles may be unequal
Correct answer is option 'A'. Can you explain this answer?
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Choose the correct statementa)Two right triangles are congruent, if hy...
Statement A: Two right triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangle.
Explanation:
To understand this statement, we need to review the concept of congruent triangles. Two triangles are said to be congruent if their corresponding sides and angles are equal. In other words, all corresponding sides and angles of two congruent triangles are identical.
In a right triangle, the side opposite the right angle is called the hypotenuse. Let's consider two right triangles, Triangle ABC and Triangle DEF.
Step 1: Identify the given information:
- Triangle ABC is a right triangle with hypotenuse AB and side AC.
- Triangle DEF is a right triangle with hypotenuse DE and side DF.
Step 2: Hypothesis:
If Triangle ABC and Triangle DEF are congruent, then the following conditions must be satisfied:
- The hypotenuse of Triangle ABC (AB) is equal to the hypotenuse of Triangle DEF (DE).
- One side of Triangle ABC (AC) is equal to one side of Triangle DEF (DF).
Step 3: Applying the hypothesis:
Let's assume that AB = DE and AC = DF.
Step 4: Conclusion:
If the hypotenuse and a side of one right triangle (Triangle ABC) are respectively equal to the hypotenuse and a side of another right triangle (Triangle DEF), then the two triangles are congruent. This means that all corresponding sides and angles of Triangle ABC and Triangle DEF are equal.
Example:
To illustrate this, consider the following example:
- Triangle ABC: AB = 5 cm, AC = 4 cm
- Triangle DEF: DE = 5 cm, DF = 4 cm
In this case, the hypotenuse AB of Triangle ABC is equal to the hypotenuse DE of Triangle DEF, and the side AC of Triangle ABC is equal to the side DF of Triangle DEF. Therefore, Triangle ABC and Triangle DEF are congruent.
Conclusion:
Statement A is correct. Two right triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangle.
Explanation:
To understand this statement, we need to review the concept of congruent triangles. Two triangles are said to be congruent if their corresponding sides and angles are equal. In other words, all corresponding sides and angles of two congruent triangles are identical.
In a right triangle, the side opposite the right angle is called the hypotenuse. Let's consider two right triangles, Triangle ABC and Triangle DEF.
Step 1: Identify the given information:
- Triangle ABC is a right triangle with hypotenuse AB and side AC.
- Triangle DEF is a right triangle with hypotenuse DE and side DF.
Step 2: Hypothesis:
If Triangle ABC and Triangle DEF are congruent, then the following conditions must be satisfied:
- The hypotenuse of Triangle ABC (AB) is equal to the hypotenuse of Triangle DEF (DE).
- One side of Triangle ABC (AC) is equal to one side of Triangle DEF (DF).
Step 3: Applying the hypothesis:
Let's assume that AB = DE and AC = DF.
Step 4: Conclusion:
If the hypotenuse and a side of one right triangle (Triangle ABC) are respectively equal to the hypotenuse and a side of another right triangle (Triangle DEF), then the two triangles are congruent. This means that all corresponding sides and angles of Triangle ABC and Triangle DEF are equal.
Example:
To illustrate this, consider the following example:
- Triangle ABC: AB = 5 cm, AC = 4 cm
- Triangle DEF: DE = 5 cm, DF = 4 cm
In this case, the hypotenuse AB of Triangle ABC is equal to the hypotenuse DE of Triangle DEF, and the side AC of Triangle ABC is equal to the side DF of Triangle DEF. Therefore, Triangle ABC and Triangle DEF are congruent.
Conclusion:
Statement A is correct. Two right triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangle.
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Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer?
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Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer?.
Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer?.
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ample number of questions to practice Choose the correct statementa)Two right triangles are congruent, if hypotenuse and a side of one are respectively equal to the hypotenuse and a side of the other triangleb)If thee altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isoscelesc)If any two sides of a right triangle are respectively are equal to two sides of the other right triangle, then the two triangles are congruentd)Sides opposite equal angles may be unequalCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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