Let's analyze the similarity of the triangles in each question based on the information in the image.

First Pair of Triangles: $\triangle ABC$ and $\triangle DEF$

1. Side Lengths:
   • $AB = 4$, $BC = 8$, $AC = 10$
   • $DE = 2$, $EF = 5$, $DF = 4$
2. Similarity Check:
   • To determine similarity, compare the ratios of corresponding sides.
   • $\frac{AB}{DE} = \frac{4}{2} = 2$, $\frac{BC}{EF} = \frac{8}{5}$, $\frac{AC}{DF} = \frac{10}{4} = 2.5$
   • Since the side ratios are not equal, these triangles are not similar.

Second Pair of Triangles: $\triangle XYZ$ and another triangle

1. Information:
   • No side lengths or clear angles are given; only angle markings are visible.
2. Similarity Check:
   • The two triangles have two pairs of corresponding angles marked as equal.
   • By the AA (Angle-Angle) Similarity Postulate, if two angles of one triangle are equal to two angles of another, the triangles are similar.
   • Therefore, $\triangle XYZ$ is similar to the other triangle by AA similarity.

Third Pair of Triangles: $\triangle STU$ and $\triangle PQR$

1. Side Lengths:
   • $ST = 21$, $TU = 9$
   • $PQ = 6$, $QR = 14$
2. Similarity Check:
   • Comparing the ratios of the sides, $\frac{ST}{PQ} = \frac{21}{6} = 3.5$ and $\frac{TU}{QR} = \frac{9}{14} \approx 0.64$.
   • Since the ratios are not consistent, the triangles are not similar.

Summary:

• First pair: Not similar.
• Second pair: Similar by AA similarity.
• Third pair: Not similar.

Would you like further explanation on similarity criteria?

Follow-Up Questions:

1. What are the different criteria for triangle similarity?
2. How does the AA similarity postulate apply to triangles without given side lengths?
3. Can two triangles be similar if only one pair of angles is congruent?
4. How do we determine similarity using only side lengths?
5. In which cases would SSA (Side-Side-Angle) confirm triangle similarity?

Tip:

For triangle similarity, focus on identifying matching angles or proportional sides to use AA, SAS, or SSS criteria effectively.