Question

are these triangles similar?
(there are two triangles in the image, one with vertices h, i, j (angle at h is 98°, angle at j has a red mark) and the other with vertices e, f, g (angle at f is 98°, angle at g has a red mark). the options are yes and no.)

Explanation:

Step1: Identify matching angles

In $\triangle HIJ$, $\angle H = 98^\circ$, $\angle J$ is marked. In $\triangle EFG$, $\angle F = 98^\circ$, $\angle G$ is marked (matches $\angle J$).

Step2: Apply AA similarity rule

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, $\angle H = \angle F = 98^\circ$, and $\angle J = \angle G$ (marked congruent). Thus, the third angles will also be equal.

Step3: Conclude similarity

By AA (Angle-Angle) similarity criterion, $\triangle HIJ \sim \triangle EFG$.

Answer:

yes