Pentagon JKLMN
 is similar to pentagon ABCDE
.
 



If pentagon JKLMN is similar to pentagon ABCDE, this means that the two pentagons have the same shape but may differ in size. Specifically, all corresponding angles are equal, and the ratios of the lengths of corresponding sides are constant. This ratio is called the **scale factor**.

### Important Properties of Similar Polygons:
1. **Corresponding angles** are equal: ∠J = ∠A, ∠K = ∠B, ∠L = ∠C, ∠M = ∠D, and ∠N = ∠E.
2. **Corresponding sides** are proportional: 
   \[
   \frac{JK}{AB} = \frac{KL}{BC} = \frac{LM}{CD} = \frac{MN}{DE} = \frac{NJ}{EA}
   \]
   This constant ratio is the **scale factor** between the two pentagons.

### Example:
If you know the lengths of sides of pentagon ABCDE and pentagon JKLMN, you can find the scale factor and use it to calculate unknown side lengths or check for the proportionality of the sides.

### Would you like a specific problem involving these pentagons to work through, or any further details on the properties of similar polygons?

#### 5 Related Questions:
1. How do you find the scale factor between two similar polygons?
2. If pentagon ABCDE has a perimeter of 50 units and pentagon JKLMN has a perimeter of 30 units, what is the scale factor?
3. Can two polygons with different numbers of sides be similar? Why or why not?
4. If the scale factor between pentagon JKLMN and pentagon ABCDE is 2:1, and side AB = 5 units, what is the length of side JK?
5. How does the similarity of two polygons affect their areas?

**Tip:** The ratio of the areas of two similar polygons is the square of the scale factor.

Pentagon JKLMN is similar to pentagon ABCDE.

Explore the properties of similar pentagons JKLMN and ABCDE, including the concept of corresponding angles, proportional side lengths, and the scale factor. Learn how to apply these properties to solve geometric problems. Suitable for students in Grades 8-10.

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