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Which shows two triangles that are congruent by the SSS congruence theorem? Triangles A B C and D E C are connected at point C. Angles A B C and C E D are right angles. The lengths of sides A B and E D are congruent. Triangles A B C and D E C are connected at point C. The lengths of sides A B and D E are congruent. The lengths of sides B C and C D are congruent. Triangles A B C and D E C are connected at point C. The lengths of sides A C and C E are congruent. Angles B A C and C E D are congruent. Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent. The lengths of B C and D C are congruent.

User Markus AO
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2 Answers

7 votes

Answer:

The last case shows that the two triangles are congruent by SSS congruency theorem

Explanation:

Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent. The lengths of B C and D C are congruent.

With this case. You have sides AB = AD, BC = DC, and then can conclude that AC= AC by reflexive property because AC is the common side.

so triangle ABC = triangle ADC by SSS congruency

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CASE 1.) Triangles A B C and D E C are connected at point C. Angles A B C and C E D are right angles. The lengths of sides A B and E D are congruent. ---- You would only know one pair of sides and one pair of angles that are congruent.

CASE 2.) Triangles A B C and D E C are connected at point C. The lengths of sides A B and D E are congruent. The lengths of sides B C and C D are congruent. ----- You would only know 2 pairs of congruent sides.

CASE 3.)Triangles A B C and D E C are connected at point C. The lengths of sides A C and C E are congruent. Angles B A C and C E D are congruent. ---- You would only know a pair of angles and a pair of sides. Not enough for congruency.

CASE 4.) Triangles A B C and A D C share common side A C. The lengths of A B and A D are congruent. The lengths of B C and D C are congruent.

User CursedChico
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7.8k points
5 votes

Answer:

d

Explanation:

User Said  Kholov
by
8.2k points

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