Which shows two triangles that are congruent by the SSS congruence theorem?

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ahill56789 ahill56789

05-07-2017
Mathematics

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Which shows two triangles that are congruent by the SSS congruence theorem?

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thatguy71373 thatguy71373 · Answer 1 · 2017-07-05T16:35:17+02:00

thatguy71373 thatguy71373

05-07-2017

It would be the last one, because the base of the first triangle matches up with the second triangle and the markings on the other sides indicate that they are the same. That being said, there are no curvy markings which indicate only sides.

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eudora eudora · Answer 2 · 2021-10-26T18:33:52+02:00

SSS congruence theorem (Side-Side-Side) states that if all the sides of two triangles are equal in measure both the triangles will be congruent.

By SSS congruence theorem, figure 4 will show the given triangles congruent.

By applying SSS theorem of congruence in figure - 1,

In ΔABC and ΔDEC,

AB ≅ DE (Given)

But other two sides are not equal.

Therefore, ΔABC and ΔDEC are not congruent.

By applying SSS theorem of congruence in figure - 2,

In ΔABC and ΔEDC,

AB ≅ ED (Given)

BC ≅ DC (Given)

But third side of both the triangles are not equal.

Therefore, ΔABC and ΔEDC are not congruent.

By applying SSS theorem of congruence in figure - 3,

In ΔABC and ΔEDC,

AC ≅ EC (Given)

But other two sides of these triangles are not equal.

Therefore, ΔABC and ΔEDC are not congruent.

By applying SSS theorem of congruence in figure - 4,

In ΔABC and ΔADC,

AB ≅ AD (Given)

BC ≅ DC (Given)

AC ≅ AC (Reflexive property)

Therefore, ΔABC ≅ ΔADC

Hence, In figure - 4, given triangles ΔABC and ΔADC will be congruent.

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