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In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB?
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In the given fig,abc is a triangle in which angleA = angleB and AD=BE....
Suppose ABC be a Triangle where Ang.A=Ang.B and D&E are the points on ur figure..Then Clearly AC=BCNOW,we have AD=BEso,AC-AD=BC-BEI.E.CD=CEOR,CD/CE=1ALSO,AC/BC=1SO,CD/CE=AC/BCOR,CD/AC=CE/BCNOW,IN TRIANGLE.CDE AND TRIANGLE.CABCD/AC=CE/BCALSO,ANG.DCE=ANG.ACB (COMMON)SO.BOTH TRIANGLE ARE SIMILAR SO,BY B.P.T...DE PARALLEL AB..
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In the given fig,abc is a triangle in which angleA = angleB and AD=BE....
Proof:
Given: In triangle ABC, angle A = angle B and AD = BE.
To prove: DE || AB.
Proof:
Step 1: Draw a line segment CF parallel to DE, intersecting AB at F.
Step 2: Now, we need to prove that DE || AB. To prove this, we will prove that angles ADE and ACF are equal.
Step 3: In triangle ABD, angle A = angle B (Given).
Step 4: In triangle ADE, angle A = angle DAE (Angles opposite to equal sides are equal).
Step 5: In triangle ACF, angle A = angle CAF (Angles opposite to equal sides are equal).
Step 6: From Step 4 and Step 5, we have angle DAE = angle CAF.
Step 7: In triangle ADE, angle DAE = angle ADE (Angle sum property of a triangle).
Step 8: From Step 6 and Step 7, we have angle ADE = angle CAF.
Step 9: From Step 8, we can conclude that angles ADE and ACF are equal.
Step 10: Now, since angles ADE and ACF are equal, it implies that DE is parallel to CF (Alternate Interior Angles Theorem).
Step 11: But CF is parallel to DE, so we can conclude that DE is parallel to AB (Transitive Property of Parallel Lines).
Step 12: Hence, we have proved that DE || AB.
Therefore, in triangle ABC, if angle A = angle B and AD = BE, then DE is parallel to AB.
Given: In triangle ABC, angle A = angle B and AD = BE.
To prove: DE || AB.
Proof:
Step 1: Draw a line segment CF parallel to DE, intersecting AB at F.
Step 2: Now, we need to prove that DE || AB. To prove this, we will prove that angles ADE and ACF are equal.
Step 3: In triangle ABD, angle A = angle B (Given).
Step 4: In triangle ADE, angle A = angle DAE (Angles opposite to equal sides are equal).
Step 5: In triangle ACF, angle A = angle CAF (Angles opposite to equal sides are equal).
Step 6: From Step 4 and Step 5, we have angle DAE = angle CAF.
Step 7: In triangle ADE, angle DAE = angle ADE (Angle sum property of a triangle).
Step 8: From Step 6 and Step 7, we have angle ADE = angle CAF.
Step 9: From Step 8, we can conclude that angles ADE and ACF are equal.
Step 10: Now, since angles ADE and ACF are equal, it implies that DE is parallel to CF (Alternate Interior Angles Theorem).
Step 11: But CF is parallel to DE, so we can conclude that DE is parallel to AB (Transitive Property of Parallel Lines).
Step 12: Hence, we have proved that DE || AB.
Therefore, in triangle ABC, if angle A = angle B and AD = BE, then DE is parallel to AB.
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In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB?
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In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB?.
In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given fig,abc is a triangle in which angleA = angleB and AD=BE.prove that DE || AB?.
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