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 the three corresponding sides of another triangle, then the two triangles are congruent.

Step2: Analyze Each Option

• First Option:
• There are right - angles (which is an angle, not a side for SSS consideration). We need to check side - side - side equality. Just having right - angles and one pair of sides marked equal (by the tick) is not sufficient for SSS.
• Second Option:
• Let's assume the sides. If we consider \(\triangle ABC\) and \(\triangle CDE\). We can see that \(AB = CD\) (marked with one tick), \(AC=CE\) (common - sense from the figure's side - length markings in terms of SSS structure), and \(BC = DE\) (marked with two ticks). So, by SSS, \(\triangle ABC\cong\triangle CDE\).
• Third Option:
• There is an angle marked (which is for SAS or ASA, not SSS). SSS requires three pairs of sides. Here, we cannot confirm three pairs of side equalities just from the given markings.
• Fourth Option:
• There is only one triangle shown. We need two triangles for congruence.

Answer:

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