Similarity Criteria Math Example 1

Solution

1. 1
   Step 1: List the angle pairs: $\angle A = \angle D = 40°$, $\angle B = \angle E = 60°$, $\angle C = \angle F = 80°$.
2. 2
   Step 2: All three angles match. However, for similarity, we only need two angles — the third is determined since angles sum to 180°.
3. 3
   Step 3: The AA (Angle-Angle) criterion states: if two angles of one triangle equal two angles of another, the triangles are similar.
4. 4
   Step 4: Conclude: $\triangle ABC \sim \triangle DEF$ by AA.