Question

are the triangles similar? why?
52°
48°
not similar. the triangles only have one pair of congruent angles.
similar, the total number of degrees in each triangle is 180.
similar, the triangles have three congruent angles.
not similar. the sides have different lengths.

Explanation:

First, calculate the missing angles in each right triangle. For the first triangle, the right angle is $90^\circ$, one angle is $48^\circ$, so the third angle is $180^\circ - 90^\circ - 48^\circ = 42^\circ$. For the second triangle, the right angle is $90^\circ$, one angle is $52^\circ$, so the third angle is $180^\circ - 90^\circ - 52^\circ = 38^\circ$. Now compare the angles: the first triangle has angles $90^\circ, 48^\circ, 42^\circ$; the second has $90^\circ, 52^\circ, 38^\circ$. Only one pair of angles (the right angles) are congruent. Triangles need at least two congruent corresponding angles (AA similarity criterion) to be similar, so these triangles are not similar.

Answer:

Not similar. The triangles only have one pair of congruent angles.