## 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.

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### 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.