1. **State the problem:** We need to name two similar triangles from the given diagram and explain why they are similar. 2. **Identify the triangles:** The triangles mentioned are ABE and CDE. 3. **Recall similarity criteria:** Triangles are similar if they have: - Corresponding angles equal (AA criterion), or - Corresponding sides in proportion (SSS or SAS criteria). 4. **Analyze given angles:** - Triangle ABE has angles 47° at A and 55° at B. - Triangle CDE has angle 42° at D. 5. **Find the third angle in triangle ABE:** $$\text{Angle } E = 180^\circ - 47^\circ - 55^\circ = 78^\circ$$ 6. **Find the third angle in triangle CDE:** We know angle D = 42°. Since E is the intersection point of diagonals, angle E in triangle CDE corresponds to angle E in triangle ABE. 7. **Check angle correspondence:** - Angle E is common to both triangles. - Angles at A (47°) and D (42°) are not equal, but if the problem implies angle BDE = 55°, then angles at B and D correspond. 8. **Conclusion:** Triangles ABE and CDE are similar by AA similarity criterion because they share angle E and have two pairs of equal angles. **Final answer:** Triangles ABE and CDE are similar by AA similarity because they have two pairs of equal angles.