Question

triangle jkl is reflected across the y - axis to create the image. which rigid - motion congruence will prove triangle jkl is congruent to triangle jkl? select the true statements. options not fully visible in ocr: side - side - side, side - angle - side, side - side - angle, angle - side - angle

Explanation:

Step1: Recall reflection property

A reflection is a rigid - motion. Rigid motions preserve side - lengths and angle - measures.

Step2: Understand congruence criteria

Since side - lengths and angle - measures are preserved in a reflection, corresponding sides and angles of the original triangle $\triangle{JKL}$ and its reflected image are equal.
For two triangles to be congruent, we can use the Side - Side - Side (SSS) criterion (if all three pairs of corresponding sides are equal), Side - Angle - Side (SAS) criterion (if two pairs of corresponding sides and the included angle are equal), Angle - Side - Angle (ASA) criterion (if two pairs of corresponding angles and the included side are equal), Angle - Angle - Side (AAS) criterion (if two pairs of corresponding angles and a non - included side are equal), and Hypotenuse - Leg (HL) for right - triangles. In the case of a reflection, all of these criteria can be satisfied because of the preservation of side - lengths and angle - measures. For example, if we consider the three sides of the triangle, the lengths of the sides of $\triangle{JKL}$ and its reflected image are the same, so SSS can prove congruence.

Answer:

All of the congruence criteria (Side - Side - Side, Side - Angle - Side, Angle - Side - Angle, Side - Angle - Side, Angle - Side - Angle) can prove that triangle $JKL$ is congruent to its reflected image.