Question

3 multiple choice 1 point determine if the triangles can be proved congruent, if possible, by sss, sas, asa, aas, or hl. hl congruence sas congruence sss congruence asa congruence not congruent aas congruence

Explanation:

Step1: Analyze the triangle markings

The two triangles share a common side (the vertical segment). The other two sides of each triangle are marked as equal (the tick marks on the slanted sides). So we have three pairs of equal sides: two marked sides and the common side.

Step2: Recall congruence criteria

SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are equal to three corresponding sides of another triangle, the triangles are congruent. Here, we have three equal sides (the two marked sides and the common side), so the triangles satisfy SSS. SAS would require two sides and the included angle, HL is for right triangles (and here the angle is a right angle? Wait, no, wait. Wait, the angle between the two sides: the two marked sides and the included angle (the angle between them). Wait, no, the common side is the vertical one, and the two marked sides are the other two. Wait, maybe I made a mistake earlier. Wait, the angle between the two marked sides and the common side: the two triangles have a common side, two equal sides (the marked ones), and the included angle (the angle between the marked side and the common side) – no, wait, the angle between the two marked sides is the angle at the bottom vertex, and the common side is the vertical. Wait, no, let's re - examine. The two triangles: let's call them \(\triangle ABC\) and \(\triangle ABD\), with \(AB\) as the common side, \(AC = AD\) (marked), and \(BC=BD\)? No, wait, the diagram shows two triangles with a common side (the vertical line), and the other two sides (the ones with tick marks) are equal, and the angle between the equal sides and the common side: wait, the angle between the two equal sides (the ones with ticks) and the common side (the vertical) – no, the angle between the two equal sides is the angle at the vertex where they meet, and the common side is the vertical. Wait, no, actually, the two triangles have: side 1: equal (marked), side 2: common side (equal), side 3: equal (marked). So three sides equal, so SSS. But wait, also, the angle between the two equal sides (the marked ones) and the common side: the angle between the marked side and the common side – no, the included angle for SAS would be the angle between the two sides. Wait, maybe the initial analysis was correct. Since we have three sides equal (the two marked sides and the common side), SSS is satisfied.

Answer:

SSS Congruence (the option with the radio button selected, which is the third option: SSS Congruence)