Geometric means Theorem

The size of the altitude drawn from the vertex that the best angle of the best triangle to its hypotenuse is the geometric mean in between the procedures of the two segments the the hypotenuse.

You are watching: What is the length of the altitude drawn to the hypotenuse

*

Geometric Mean

This theorem allows you to uncover the size of a segment of the hypotenuse given the length of the altitude and also the length of the other segment of the hypotenuse. Girlfriend can also use this to organize to uncover the length of the altitude given the length of the segments of the hypotenuse.

*

Quick Quiz

Find the altutude.

*

Start through substituting in the well-known values.

*

Answer: 4, h

Use the overcome product home to get rid of the fractions.

h2 = (4) ( ___ )

Answer: 9

Simplify

h2 = ___

Answer: 36

Take the square root of each side and simplify.

*

h = ___

Answer: 6

Similar right Triangles

Consider the ratios the the three triangles in ~ the start of the lesson.

*

Geometric average Theorem

This theorem enables you to discover the size of a segment of the hypotenuse offered the size of the adjacent leg and the length of the various other segment the the hypotenuse. Friend can likewise use this to organize to discover the size of a leg the the triangle offered the size of the segments of the hypotenuse.

See more: What Is Next In This Series? 1, 4, 10, 19, 31, _ ? Centered Triangular Number

Similar ideal Triangles

If the altitude is drawn to the hypotenuse that a right triangle, climate the measure up of a leg the the ideal triangle is the geometric mean between the measure up of the hypotenuse and the segment of the hypotenuse adjacent to that leg.