Question

decide whether the triangles are similar or not. if yes, give the rule that justifies your answer. 7. 8.

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. In the first - pair of triangles, the non - right angles where the lines intersect are vertical angles and thus equal. Also, both triangles have a right angle.

Step2: Apply AA (Angle - Angle) similarity rule

Since two angles of one triangle are equal to two angles of the other triangle, by the AA similarity rule, the triangles are similar.

Step3: For the second - pair of triangles

The two angles marked as equal are corresponding angles. Also, the two triangles share the same angle at the top vertex.

Step4: Apply AA similarity rule again

Since two angles of one triangle are equal to two angles of the other triangle, by the AA similarity rule, the triangles are similar.

Answer:

1. Yes, AA (Angle - Angle) similarity rule.
2. Yes, AA (Angle - Angle) similarity rule.