Question

eli shows that triangle a is congruent to triangle b by rotating triangle a around point k and then translating it so it matches up with triangle b exactly. which conclusion can be drawn from elis transformations?
if right triangles have congruent hypotenuses and one pair of congruent legs, the triangles are congruent.
if two triangles have right angles, all pairs of corresponding sides are congruent.
if one pair of angles is congruent, then all pairs of angles are congruent.
if two pairs of sides and the included angle are congruent, the triangles are congruent.

Explanation:

Step1: Recall congruent triangle theorems

For right - angled triangles, the Hypotenuse - Leg (HL) theorem states that if the hypotenuses and one pair of congruent legs of two right - angled triangles are congruent, then the triangles are congruent.

Step2: Analyze the given triangles

In triangle \(A\) (\(\triangle TSK\)) and triangle \(B\) (\(\triangle GIH\)), they are right - angled triangles. Eli shows a rotation and translation (rigid motions). Rigid motions preserve side lengths and angles. If we assume the conditions of the HL theorem (since they are right - angled and from the congruence shown by the transformation, we can check the side - side relationships). The key is the HL theorem for right - angled triangles.

Answer:

If right triangles have congruent hypotenuses and one pair of congruent legs, the triangles are congruent.