Question

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

Explanation:

Step1: Recall SSS Congruence

SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent. We need to check each figure for three pairs of equal - length sides (marked by tick marks).

Step2: Analyze the second figure

In the second figure (the middle - upper one among the four, with points A, B, C, D, E), we can see that:

• \(AB = DE\) (marked with one tick), \(BC=CD\) (marked with two ticks), and \(AC = EC\) (since C is the mid - point of AE, so \(AC = EC\)). So, in \(\triangle ABC\) and \(\triangle EDC\), we have three pairs of equal sides: \(AB = DE\), \(BC = DC\), and \(AC=EC\). This satisfies the SSS congruence criterion.

Let's check the other figures:

• First figure: It seems to have two pairs of equal sides (maybe SAS - like, with a common side and two other sides, but not three distinct pairs for SSS).
• Third figure: It has right angles and one pair of equal sides, more like HL (Hypotenuse - Leg) or AAS/ASA, not SSS.
• Fourth figure: It has angles and one pair of equal sides, more like ASA or SAS, not SSS.

Answer:

The second graph (the one with points A, B, C, D, E)