Question

triangle jkl is reflected across the y - axis to create the image, triangle jkl. which criteria for triangle congruence will prove triangle jkl is congruent to triangle jkl? select the three that apply. side side angle side side side angle side angle angle angle angle side angle side

Explanation:

Step1: Recall congruence criteria

The main triangle - congruence criteria are Side - Side - Side (SSS), Side - Angle - Side (SAS), Angle - Side - Angle (ASA), and Angle - Angle - Side (AAS). Side - Side - Angle (SSA) is not a valid congruence criterion, and Angle - Angle - Angle (AAA) only shows similarity, not congruence.

Step2: Analyze reflection property

A reflection is a rigid transformation. When a triangle is reflected across the y - axis, the corresponding sides and angles of the original triangle and its image are equal.

• For SSS: The lengths of the sides of $\triangle{JKL}$ are equal to the lengths of the corresponding sides of $\triangle{J'K'L'}$ because reflection preserves side - lengths.
• For SAS: The lengths of two sides and the included angle of $\triangle{JKL}$ are equal to the lengths of the corresponding two sides and the included angle of $\triangle{J'K'L'}$ since reflection preserves lengths and angles.
• For ASA: The measures of two angles and the included side of $\triangle{JKL}$ are equal to the measures of the corresponding two angles and the included side of $\triangle{J'K'L'}$ as reflection preserves angle - measures and lengths.

Answer:

B. Side Side Side
C. Angle Side Angle
E. Side Angle Side