Question

which shows two triangles that are congruent by the sss congruence theorem?

Explanation:

Step1: Recall SSS Congruence Theorem

SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Step2: Analyze the first option

In the first option, we have right - angled triangles. Let's assume the equal - marked sides. But we need to check all three sides. The vertical sides (BC and EC) are equal (marked), the hypotenuses (AC and DC) are equal (marked), and the right - angled sides (AB and DE) are equal (marked). So, by SSS, the two triangles \( \triangle ABC\) and \( \triangle DEC\) are congruent.

Step3: Analyze the second option

In the second option, we cannot confirm that all three pairs of sides are equal. The side \(AC\) and \(CE\) are not marked as equal.

Step4: Analyze the third option

In the third option, we cannot confirm that all three pairs of sides are equal. There is no information about the equality of all three pairs of sides.

Step5: Analyze the fourth option

In the fourth option, there is only one triangle shown. So, it cannot be used to show SSS congruence between two triangles.

Answer:

The first option shows two triangles that are congruent by the SSS congruence theorem.