Question

choose the triangle shortcut that can be used to state the triangles below are congruent.

triangles with markings: triangle xz (with 59° at x, one side marked) and triangle q r (with 59° at the bottom left, one side marked, another side with two marks)

choose
the triangles are not congruent.
angle angle side
angle side angle
side angle side
side side side
hypotenuse leg

Explanation:

1. Identify matching parts: In $\triangle XYZ$ and $\triangle QRP$, $\angle X = \angle P = 59^\circ$, side $XZ$ (one mark) = side $PR$ (one mark), side $XY$ (unmarked) corresponds to side $PQ$ (two marks, which are not equal to an unmarked side).
2. Check congruence rules: The equal angle is adjacent to one equal side, but the second side associated with the angle is not equal. None of the valid congruence shortcuts (AAS, ASA, SAS, SSS, HL) are satisfied because the corresponding sides around/related to the equal angle do not match appropriately to meet a rule.

Answer:

The triangles are not congruent.