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We are given that triangles \( \triangle PQR \cong \triangle LJK \), which means corresponding sides and angles are equal. The goal is to find the length of side PR.

### Key Information:
1. \( PR = 2x + 6 \) (side of \( \triangle PQR \))
2. \( JL = 10 \) units (side of \( \triangle LJK \), corresponding to \( PR \))
3. \( LK = 3x - 6 \) (side of \( \triangle LJK \))

Since \( \triangle PQR \cong \triangle LJK \), the corresponding sides are equal. Therefore, the side PR corresponds to JL:
\[
PR = JL
\]
Thus, we set up the equation:
\[
2x + 6 = 10
\]
Now, solve for \( x \):
\[
2x = 10 - 6 = 4
\]
\[
x = \frac{4}{2} = 2
\]

### Find PR:
Substitute \( x = 2 \) into the expression for \( PR \):
\[
PR = 2(2) + 6 = 4 + 6 = 10 \text{ units}
\]

Thus, the length of side PR is **10 units**.

Would you like more details or further clarification?

Here are some additional related questions:
1. What is the significance of congruent triangles in geometry?
2. How would the solution change if the value of \( JL \) were different?
3. What theorem helps us conclude that the triangles are congruent?
4. How do we know that corresponding sides are equal in congruent triangles?
5. How could you verify the equality of other corresponding sides, such as \( QR \) and \( JK \)?

**Tip**: When working with congruent triangles, always check the corresponding parts carefully to ensure accuracy.

Given that ΔPQR ≅ ΔLJK, PR=2x+6, JL=10 units, LK=3x-6, find the measure of side PR.

Solve for the length of side PR in congruent triangles ΔPQR and ΔLJK. Given PR=2x+6, JL=10 units, and LK=3x-6, learn how to use the properties of congruent triangles and algebra to find the solution.

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