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The problem involves an equilateral triangle \( \triangle JKL \) where \( KM \perp JL \). Based on this setup:

1. Since \( \triangle JKL \) is equilateral, all three sides are equal in length: \( JK = KL = JL \).
2. The line segment \( KM \) is perpendicular to \( JL \), indicating that it bisects \( JL \) at point \( M \), making \( JM = ML \).
3. Since \( \triangle JKL \) is equilateral, the angles are all 60°. The line \( KM \), being perpendicular to the base, creates two smaller right triangles: \( \triangle JKM \) and \( \triangle KML \). These are 30-60-90 triangles because of the internal angles created by the equilateral triangle.

### Evaluating the options:
- **A. \( KM = 2 \cdot JM \)**: This is true for a 30-60-90 triangle, where the hypotenuse (here \( KM \)) is twice the length of the shorter leg (here \( JM \)).
- **B. \( \triangle JKM \) is a 30-60-90 triangle**: This is correct based on the geometry of the equilateral triangle.
- **C. \( JK = KM \)**: This is false, as \( JK \) is a side of the equilateral triangle, while \( KM \) is the height, which is not equal to a side.
- **D. \( \triangle JKM \) is a 45-45-90 triangle**: This is false, as it is a 30-60-90 triangle, not a 45-45-90 triangle.

### Correct Answer:
The correct statement is **B: \( \triangle JKM \) is a 30-60-90 triangle**.

Would you like further details on how to solve 30-60-90 triangles or any other clarifications?

Here are five related questions:
1. How do you calculate the length of \( KM \) in a 30-60-90 triangle?
2. Why does \( KM \) bisect the base \( JL \) in an equilateral triangle?
3. How do we derive the properties of a 30-60-90 triangle?
4. What is the formula for the height of an equilateral triangle?
5. How do right triangles form within equilateral triangles?

**Tip**: In a 30-60-90 triangle, the longer leg is \( \sqrt{3} \) times the shorter leg!

In the diagram below, △JKL is an equilateral triangle and KM ⊥ JL. Which statement must be true?

This geometry problem involves analyzing an equilateral triangle where one altitude forms a 30-60-90 triangle. Learn the properties of equilateral triangles and how to solve for side lengths using key theorems.

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