Question

27 how are these triangles similar? a aa b sas c not similar d sss

Explanation:

Step1: Find the third angle of the first triangle

In a right - angled triangle (angle = \(90^{\circ}\)), using the angle - sum property of a triangle (\(180^{\circ}\)). Let the third angle be \(x\). Then \(x+90^{\circ}+52^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(90^{\circ}+52^{\circ})=38^{\circ}\).

Step2: Check the similarity criterion

The first triangle has angles \(90^{\circ},52^{\circ},38^{\circ}\) and the second triangle has angles \(90^{\circ},38^{\circ}\). By AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar), since two pairs of angles (\(90^{\circ}\) and \(38^{\circ}\)) are equal.

Answer:

A. AA