key term - Leg

Definition

In the context of geometry, a leg is one of the sides of a triangle or rectangle. It refers to the straight line segments that form the shape, particularly in the discussion of the Pythagorean Theorem and solving applications involving these geometric figures.

5 Must Know Facts For Your Next Test

1. The legs of a right triangle are the two sides that form the right angle, and they are always perpendicular to each other.
2. In a rectangle, the legs are the two equal-length sides that are perpendicular to each other.
3. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
4. Knowing the lengths of the legs of a right triangle allows you to calculate the length of the hypotenuse using the Pythagorean Theorem.
5. The legs of a triangle or rectangle are essential for solving various geometric applications, such as finding missing side lengths, perimeter, and area.

Review Questions

• Explain the relationship between the legs of a right triangle and the Pythagorean Theorem.
  • The legs of a right triangle are the two sides that form the right angle. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the two legs. This means that if you know the lengths of the two legs, you can use the Pythagorean Theorem to calculate the length of the hypotenuse, which is a crucial step in solving many geometric applications.
• Describe how the legs of a rectangle are used to solve geometric applications.
  • In a rectangle, the legs are the two equal-length sides that are perpendicular to each other. Knowing the lengths of the legs allows you to calculate the perimeter of the rectangle by adding the lengths of all four sides. Additionally, the lengths of the legs can be used to find the area of the rectangle by multiplying the lengths of the two legs. Understanding the properties of the legs in a rectangle is essential for solving various geometric applications, such as finding missing side lengths, perimeter, and area.
• Analyze how the concept of legs in triangles and rectangles is connected to the broader topic of solving geometry applications.
  • The concept of legs in triangles and rectangles is fundamental to solving a wide range of geometry applications. The legs, along with the other sides and angles of these shapes, provide the necessary information to apply various geometric principles and formulas, such as the Pythagorean Theorem, perimeter calculations, and area calculations. By understanding the relationships between the legs and the other components of triangles and rectangles, students can develop the skills to solve complex geometric problems involving these shapes, which are essential for success in applications-based geometry assessments.

Related terms

Hypotenuse:

The longest side of a right triangle, which is opposite the right angle.

Altitude: The perpendicular distance from the base of a triangle to the opposite vertex or side.

Base:

The side of a triangle or rectangle that is considered the bottom or foundation of the shape.