Identifying Parts of a Right Triangle: Legs and Hypotenuse
Grade 8 math students learn to identify the legs and hypotenuse of a right triangle. The legs (a and b) form the right angle, while the hypotenuse (c) is opposite the right angle and is always the longest side. This foundational skill is required before applying the Pythagorean Theorem. Covered in Big Ideas Math, Course 3, Chapter 7: Real Numbers and the Pythagorean Theorem.
Key Concepts
Property In a right triangle, the legs (sides $a$ and $b$) are the two sides that form the right angle. The hypotenuse (side $c$) is the side opposite the right angle and is always the longest side.
Examples In a right triangle like $\Delta RST$ (where $\angle S = 90^\circ$), the legs are $\overline{RS}$ and $\overline{ST}$ because they form the 90° angle. The hypotenuse is $\overline{RT}$ because it is the longest side across from the 90° angle. A right triangle has side lengths of 8 cm, 15 cm, and 17 cm. The longest side is 17 cm, so it is the hypotenuse. The other two sides, 8 cm and 15 cm, are the legs. In a triangle where the sides adjacent to the right angle measure $x$ and $y$, and the third side is $z$, the sides $x$ and $y$ are the legs. The side $z$ is the hypotenuse.
Common Questions
What is the hypotenuse of a right triangle?
The hypotenuse is the side opposite the right angle in a right triangle. It is always the longest side and is represented by c in the Pythagorean Theorem formula a^2 + b^2 = c^2.
What are the legs of a right triangle?
The legs of a right triangle are the two sides that form the right angle, labeled a and b in the Pythagorean Theorem. They are the shorter sides of the right triangle.
How do you identify the hypotenuse?
Find the right angle symbol (small square) in the triangle. The side directly across from it (which never touches the right angle) is the hypotenuse. It is always the longest side.
Which textbook covers parts of a right triangle for Grade 8?
This topic is in Big Ideas Math, Course 3, Chapter 7: Real Numbers and the Pythagorean Theorem.
What grade level covers right triangle vocabulary?
Identifying parts of a right triangle is typically covered in Grade 8 math.