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2.3 RIGHT TRIANGLES
The right angled triangle is one of the most useful shapes in all of mathematics! A right triangle is a triangle with one right angle, measuring 90°. The little square in the corner tells you that it is a right triangle.
You will learn about the different parts of a right triangle, the Pythagorean Theorem, and special right triangles.
PARTS OF A RIGHT TRIANGLE
A right triangle has one right angle. The sides of a right triangle have special names. The side opposite the right angle is the hypotenuse. The hypotenuse is always the longest side. Each side that forms the right angle is a leg.
A right triangle has side measures of 3 feet, 4 feet, and 5 feet. What is the length of the hypotenuse?
SOLUTION: The length of the hypotenuse is 5 feet. The hypotenuse is always the longest side.
Khan Academy Pythagorean Theorem Practice <--click link
Special Right Triangles
A 45° - 45° - 90° triangle is an isosceles triangle. It has two congruent angles and two congruent sides. The hypotenuse of a 45° - 45° - 90° triangle is equal to the leg √2. If you know the lengths of one side, you can find the lengths of the other two sides. You can also use a shortcut to find the lengths of the unknown sides of a 30° - 60° - 90° triangle. First, you need to identify the short leg. The short leg is always opposite the 30° angle. The 45° - 45° - 90° triangle and 30° - 60° - 90° triangle are shown below.
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