Question

which rule explains why these scalene triangles are similar?

(image of two triangles with vertices h, i, g and k, j, g; angles at i and k are 38°, angle at j is 92°)

options:
sss
sas
aa
none of the above; the triangles cannot be proven similar

Explanation:

Step1: Identify Vertical Angles

Angles at \( G \) ( \( \angle HGI \) and \( \angle JGK \)) are vertical angles, so they are equal.

Step2: Identify Given Angles

In \( \triangle HI G \), \( \angle I = 38^\circ \). In \( \triangle KJ G \), \( \angle K = 38^\circ \), so \( \angle I=\angle K \). Also, vertical angles \( \angle HGI=\angle JGK \).

Step3: Apply AA Similarity

By AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, we have two pairs of equal angles (vertical angles and \( 38^\circ \) angles), so AA rule applies.

Answer:

AA