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ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f?
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ABC is a triangle in which altitude be and CF to sides AC and ab are e...
Given:
- ABC is a triangle.
- BE and CF are altitudes of triangle ABC.
- BE = CF.
Proof:
1. Triangles ABC and ACF share a common side AC:
Since BE and CF are altitudes of triangle ABC, they are perpendicular to sides AC and AB respectively. This means that triangle ABC and triangle ACF share the common side AC.
2. Triangles ABC and ACF have a common angle at C:
Since BE and CF are perpendicular to sides AC and AB respectively, angle BAC = angle FAC, which means that triangles ABC and ACF have a common angle at C.
3. Triangles ABC and ACF have an equal side CF:
Given that BE = CF, we know that triangle ABC and triangle ACF have an equal side CF.
4. By SAS (Side-Angle-Side) congruence criterion:
Since triangles ABC and ACF share a common side, have a common angle, and have an equal side, they can be proved congruent by the SAS criterion.
Therefore, triangle ABC is congruent to triangle ACF.
- ABC is a triangle.
- BE and CF are altitudes of triangle ABC.
- BE = CF.
Proof:
1. Triangles ABC and ACF share a common side AC:
Since BE and CF are altitudes of triangle ABC, they are perpendicular to sides AC and AB respectively. This means that triangle ABC and triangle ACF share the common side AC.
2. Triangles ABC and ACF have a common angle at C:
Since BE and CF are perpendicular to sides AC and AB respectively, angle BAC = angle FAC, which means that triangles ABC and ACF have a common angle at C.
3. Triangles ABC and ACF have an equal side CF:
Given that BE = CF, we know that triangle ABC and triangle ACF have an equal side CF.
4. By SAS (Side-Angle-Side) congruence criterion:
Since triangles ABC and ACF share a common side, have a common angle, and have an equal side, they can be proved congruent by the SAS criterion.
Therefore, triangle ABC is congruent to triangle ACF.
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ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f?
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ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f?.
ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is a triangle in which altitude be and CF to sides AC and ab are equal show that triangle ABC is congruent to triangle a c f?.
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