Similar Right Triangles Formed by an Altitude

Front

What are similar right triangles?

Back

Similar right triangles are triangles that have the same shape but may differ in size. They have equal corresponding angles and their sides are in proportion.

Front

What is the altitude in a triangle?

Back

The altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.

Front

How do you find the length of the altitude in a right triangle?

Back

The length of the altitude can be found using the formula: h = (a * b) / c, where a and b are the lengths of the legs and c is the length of the hypotenuse.

Front

What is the geometric mean in the context of similar triangles?

Back

The geometric mean is the positive square root of the product of two numbers. In similar triangles, the altitude to the hypotenuse is the geometric mean of the segments it divides the hypotenuse into.

Front

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

Back

The corresponding sides of similar triangles are proportional.

Front

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

Back

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

Front

How can you use proportions to solve for missing lengths in similar triangles?

Back

You can set up a proportion using the lengths of the corresponding sides of the triangles and solve for the unknown length.

Front

What is the significance of the altitude in creating similar triangles?

Back

The altitude creates two smaller triangles that are similar to the original triangle and to each other.

Front

How do you apply the properties of similar triangles to solve for unknown lengths?

Back

By using the properties of similar triangles, you can set up equations based on the ratios of the sides to find unknown lengths.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by the formula: Area = 1/2 * base * height.