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In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC?
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In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is paral...
Proof of ∆ABD ≅ ∆FEC
1. Given information:
- AB = EF
- BC = ED
- AB || BD
- FE || EC
2. Proving ∆ABD ≅ ∆FEC:
- Since AB || BD and FE || EC, we have ∠ABD = ∠FEC (alternate interior angles)
- Additionally, AB = EF and BC = ED are given
- By ASA (Angle-Side-Angle) postulate, we can prove that ∆ABD ≅ ∆FEC
3. Explanation:
- The given information establishes the equality of corresponding sides and angles of the two triangles.
- AB = EF and BC = ED show that the corresponding sides are equal in length.
- AB || BD and FE || EC indicate that the corresponding angles are equal.
- Thus, by proving that the two triangles have two pairs of congruent angles and one pair of congruent sides, we can conclude that ∆ABD ≅ ∆FEC.
4. Conclusion:
- Therefore, based on the given information and the application of the ASA postulate, we have successfully proven that ∆ABD is congruent to ∆FEC.
1. Given information:
- AB = EF
- BC = ED
- AB || BD
- FE || EC
2. Proving ∆ABD ≅ ∆FEC:
- Since AB || BD and FE || EC, we have ∠ABD = ∠FEC (alternate interior angles)
- Additionally, AB = EF and BC = ED are given
- By ASA (Angle-Side-Angle) postulate, we can prove that ∆ABD ≅ ∆FEC
3. Explanation:
- The given information establishes the equality of corresponding sides and angles of the two triangles.
- AB = EF and BC = ED show that the corresponding sides are equal in length.
- AB || BD and FE || EC indicate that the corresponding angles are equal.
- Thus, by proving that the two triangles have two pairs of congruent angles and one pair of congruent sides, we can conclude that ∆ABD ≅ ∆FEC.
4. Conclusion:
- Therefore, based on the given information and the application of the ASA postulate, we have successfully proven that ∆ABD is congruent to ∆FEC.
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In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC?
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In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC?.
In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, AB=EF , BC=ED , ABis parallel to BD , FE is parallel to EC . prove that ∆ABD=~∆FEC?.
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