Question

example 1
determine whether each pair of triangles is similar. explain your reasoning.
1.
2.

Explanation:

Step1: Analyze first triangle pair

In $\triangle FGH$ and $\triangle KJH$:

• $\angle F = \angle K$ (given right angles)
• $\angle GHF = \angle JHK$ (vertical angles are congruent)

By AA (Angle-Angle) Similarity Criterion, two angles of one triangle are congruent to two angles of the other triangle.

Step2: Calculate missing angles for second pair

For $\triangle STR$:
Third angle $\angle R = 180^\circ - 42^\circ - 98^\circ = 40^\circ$
For $\triangle UVW$:
Third angle $\angle W = 180^\circ - 40^\circ - 98^\circ = 42^\circ$
Now, $\triangle STR$ has angles $42^\circ, 98^\circ, 40^\circ$; $\triangle UVW$ has angles $40^\circ, 98^\circ, 42^\circ$. All corresponding angles are congruent, so by AA Similarity Criterion, the triangles are similar.

Answer:

1. $\triangle FGH \sim \triangle KJH$; they are similar by the AA Similarity Criterion (one pair of right angles are congruent, and vertical angles $\angle GHF$ and $\angle JHK$ are congruent).
2. $\triangle STR \sim \triangle WVU$; they are similar by the AA Similarity Criterion (all corresponding angles are congruent: $42^\circ, 98^\circ, 40^\circ$ in both triangles).