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# In the figure AD=AE and D and E are point on BC. Such that BD =EC. Prove that AB=AC.?

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- 7 years agoFavorite Answer
first of the AED triangle is isosceles because AE=AD so that means that the angles AED=ADE. that means that also the angles AEC and ADB are congruent. now we are going to prove the congruency of the two triangles ACE and ABD. since AE=ED, EC=DB and AEC=ADB, that means that the triangles ACE and ABD are congruent which means that AB=AC

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- 7 years ago
B-----D-----A-----E-----C

1)AD=AE {given}

2)BD=EC {given}

3)Therefore, A is midpoint of line segment D and E {From 1)]

4)Add 1) & 2)

AD+BD=AE+EC

Therefore, AB =AC {From fig.]

5)Hence Proved

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