https://file.aiquickdraw.com/mathbot/file/17297862748978zi8akq2.jpg

Let's break down the problem step by step based on the provided image.

### Part (a): Complete the congruence statements.
Looking at the triangles, we can deduce the congruence between corresponding angles based on their shapes and measurements.

- \( \angle J \) corresponds to \( \angle G \).
- \( \angle K \) corresponds to \( \angle E \).
- \( \angle L \) corresponds to \( \angle F \).

So, the correct matching for the angles is:

- \( \angle J \cong \angle G \)
- \( \angle K \cong \angle E \)
- \( \angle L \cong \angle F \)

### Part (b): Find the ratios of corresponding sides.
We will calculate the ratios of the corresponding sides of the triangles. To do this, we will compare the side lengths between the two triangles.

1. For \( \frac{GF}{JK} \):
   - \( GF = 21 \), \( JK = 14 \)
   - \( \frac{GF}{JK} = \frac{21}{14} = \frac{3}{2} \)

2. For \( \frac{FE}{KL} \):
   - \( FE = 24 \), \( KL = 10 \)
   - \( \frac{FE}{KL} = \frac{24}{10} = \frac{12}{5} \)

3. For \( \frac{GE}{JL} \):
   - \( GE = 15 \), \( JL = 16 \)
   - \( \frac{GE}{JL} = \frac{15}{16} \)

### Part (c): Select the true statement.
We observe that the triangles have proportional sides (since all corresponding sides maintain a constant ratio), and the corresponding angles are congruent. Therefore, the two triangles are **similar**.

Thus, the correct statement is:  
- \( \triangle JKL \) and \( \triangle GFE \) are similar.

Let me know if you want further details or have any questions.

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Here are 5 related questions to expand on the topic:

1. How do you prove triangles are similar using the Angle-Angle (AA) criterion?
2. Can two triangles be congruent without being similar? Why or why not?
3. What are the key differences between congruent and similar triangles?
4. If a triangle's sides are scaled by a factor, what happens to its area?
5. How does the SSS (Side-Side-Side) similarity theorem work?

**Tip**: When working with triangles, always check both the angles and the proportionality of the sides to confirm similarity or congruence.

For the triangles below, use the tools to move the solid triangle exactly onto the dashed one. Complete the congruence statements, find the ratios of the sides, and determine if the triangles are similar.

This problem focuses on determining the congruence of angles and the similarity of two triangles by analyzing side ratios and angles. Explore how to prove similarity using the AA criterion and calculate the proportionality of corresponding sides.

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