Question

determine whether the triangles are similar by sas-, aa-, sss- or none. sas- aa- sss- none apply, sides are not proportional none apply, angles are not the same

Explanation:

Step1: Recall similarity - criteria

SAS (Side - Angle - Side) requires two pairs of proportional sides and the included angle equal. AA (Angle - Angle) requires two pairs of equal angles. SSS (Side - Side - Side) requires all three pairs of sides to be proportional.

Step2: Analyze given angles

In the first triangle, we have an angle of 65°. In the second triangle, we have an angle of 65° and an angle of 63°. Since the sum of angles in a triangle is 180°, in the first triangle, if one angle is 65°, and assuming we don't have information about the other two angles yet. In the second triangle, the third - angle is \(180-(65 + 63)=52^{\circ}\). We only know one pair of equal angles (the 65° angles), and we have no information about the side - lengths.

Step3: Determine similarity

Since we only have one pair of equal angles and no information about side - lengths, we cannot use SAS or SSS. And we don't have two pairs of equal angles for AA.

Answer:

none apply, angles are not the same