Question

1. if triangles abc and def have sides ab = de (3 cm), bc = ef (4 cm), and ac = df (5 cm), what can we conclude about the two triangles? the triangles are congruent by sss criteria the triangles are congruent by asa criteria the triangles are not congruent the triangles are congruent by sas criteria

Explanation:

To determine the congruence of triangles \(ABC\) and \(DEF\), we analyze the given side lengths: \(AB = DE = 3\space\text{cm}\), \(BC = EF = 4\space\text{cm}\), and \(AC = DF = 5\space\text{cm}\). The SSS (Side - Side - Side) congruence criterion states that if the three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent. Here, all three pairs of corresponding sides are equal. The ASA (Angle - Side - Angle) criterion requires two angles and the included side to be equal, and the SAS (Side - Angle - Side) criterion requires two sides and the included angle to be equal. Since we only have information about the sides (not angles), the SSS criterion applies. Also, since all corresponding sides are equal, the triangles are congruent, so the option "The triangles are not congruent" is incorrect.

Answer:

The triangles are congruent by SSS criteria