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  • In Figure, D and E are points on side BC of a triangle ABC such that BD equal to CE and AD equal to AE. Show that Triangle ABD congruent to triangle ACE.

In Figure, D and E are points on side BC of a \triangleABC such that BD = CE and AD = AE. Show that \triangleABD \cong \triangleACE.

Answers (1)

Given, ABC is triangle

BD = CE and AD = AE

Where D and E are points an side BC respectively

To prove: \triangleABD \cong \triangleACE

Proof :- AD = AE (Given)

Then \triangleADE is an isosceles triangle.

We know that if two sides of a given triangle are equal then their opposite angles are also equal.

then, \angleADE = \angleAED = q

Now from \triangleADB and \triangleAEC

\angleADB = 180° – \angleADE                      .....(1)

and \angleAEC = 180° – \angleAED                .....(2)

\Rightarrow \angleADB = 180° – q, \angleAEC = 180° – q

Then by SAS criterion of congruence

\because AD = AE                                         (given)

\angleADE = \angleAEC                                  (from above)

BD = EC                                             (given)

Þ \triangleABD \cong \triangleACE.

Hence proved.

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