Review of special and similar right triangles

Front

What is a 45°-45°-90° triangle?

Back

A 45°-45°-90° triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees. The lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

What is a 30°-60°-90° triangle?

Back

A 30°-60°-90° triangle is a right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees. The ratio of the lengths of the sides opposite these angles is 1:√3:2.

Front

How do you find the length of the hypotenuse in a 45°-45°-90° triangle?

Back

In a 45°-45°-90° triangle, the length of the hypotenuse is equal to the length of a leg multiplied by √2.

Front

How do you find the length of the longer leg in a 30°-60°-90° triangle?

Back

In a 30°-60°-90° triangle, the length of the longer leg is equal to the length of the shorter leg multiplied by √3.

Front

What is the relationship between similar triangles?

Back

Similar triangles have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

How do you set up a proportion to solve for missing sides in similar triangles?

Back

To set up a proportion, you can use the ratio of the lengths of corresponding sides of the triangles. If triangle A has sides a1, a2, and triangle B has sides b1, b2, then a1/b1 = a2/b2.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

How do you find the value of x in a right triangle using the Pythagorean theorem?

Back

To find the value of x in a right triangle, you can rearrange the Pythagorean theorem: x = √(a² + b²) if x is the hypotenuse, or x = √(c² - b²) if x is one of the legs.

Front

What is the significance of the 45°-45°-90° triangle in geometry?

Back

The 45°-45°-90° triangle is significant because it is a special case of the isosceles right triangle, which simplifies calculations involving angles and side lengths.