Question

are the triangles similar? why?

not similar. there is only one congruent angle.

similar. the measures of the non - right angles in each triangle add to 90°.

not similar. the side lengths are not proportional.

similar. the triangles are similar by the aa similarity postulate.

Explanation:

Step1: Find missing angle of first triangle

Sum of angles in triangle is $180^\circ$. For first right triangle:
$180^\circ - 90^\circ - 36^\circ = 54^\circ$

Step2: Find missing angle of second triangle

Sum of angles in triangle is $180^\circ$. For second right triangle:
$180^\circ - 90^\circ - 54^\circ = 36^\circ$

Step3: Compare corresponding angles

Both triangles have angles $90^\circ$, $36^\circ$, $54^\circ$. Two pairs of congruent angles satisfy AA Similarity.

Answer:

Similar. The triangles are similar by the AA Similarity Postulate.