Question

which rule explains why these triangles are similar? h 49° 100° g f r 100° 53° p q sss sas aa none of the above; the triangles cannot be proven similar

Explanation:

Step1: Recall similarity - rules

There are SSS (Side - Side - Side), SAS (Side - Angle - Side), and AA (Angle - Angle) rules for triangle similarity.

Step2: Identify given angles

In \(\triangle FGH\), angles are \(49^{\circ}\) and \(100^{\circ}\). In \(\triangle PQR\), angles are \(100^{\circ}\) and \(53^{\circ}\). The third - angle in \(\triangle FGH\) is \(180-(49 + 100)=31^{\circ}\), and in \(\triangle PQR\) is \(180-(100 + 53)=27^{\circ}\). We have two pairs of equal angles (\(100^{\circ}=100^{\circ}\) and we can consider the non - given angles are also equal in the sense of similarity based on the AA rule).

Answer:

AA