Question

triangle congruence: asa and aas
which of these triangle pairs can be mapped to each other using a reflection and a translation?
image of four sets of triangle pairs

Explanation:

Step1: Recall Reflection/Translation Effects

Reflection flips a figure over a line, translation slides it. Both preserve shape, size, and angle/side congruence. We need triangle pairs with corresponding congruent angles/sides, and orientation allowing reflection + translation to map one to the other.

Step2: Analyze Each Pair

• First Pair: Check angles/sides. The right angles, marked sides, and marked angles. But orientation? Maybe not.
• Second Pair: Triangles have right angles, marked sides, and marked angles. A reflection over a vertical line (to flip one triangle) then translation (to move it) could map them. Corresponding parts (right angle, marked side, marked angle) are congruent, matching ASA/AAS.
• Third Pair: Orientation and position don't align with reflection + translation as easily.
• Fourth Pair: Triangles are rotated, not just reflected/translated.

Answer:

The Middle Graph (Second Triangle Pair)