12.4 Similar Right Triangles

Front

What is a similar triangle?

Back

A triangle that has the same shape as another triangle but may differ in size. The corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What is the geometric mean of two numbers a and b?

Back

The geometric mean is the square root of the product of two numbers, calculated as √(a*b).

Front

How do you find the length of a side in a right triangle using 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

What is the relationship between the sides of similar right triangles?

Back

The ratios of the lengths of corresponding sides of similar right triangles are equal.

Front

How can you use proportions to solve for an unknown side in similar triangles?

Back

Set up a proportion using the lengths of corresponding sides from the two triangles and solve for the unknown side.

Front

What is the formula for finding the area of a right triangle?

Back

The area (A) of a right triangle is given by the formula A = (1/2) * base * height.

Front

If two triangles are similar, what can be said about their angles?

Back

All corresponding angles of similar triangles are equal.

Front

What is the significance of the 30-60-90 triangle in geometry?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, which helps in solving problems involving these angles.

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

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

Back

The length of the hypotenuse is equal to the length of a leg multiplied by √2.