Similar Right Triangles

Similar Right Triangles

Notes

Please add this to your notebook!

- All three triangles are similar if you have a right triangle with an altitude drawn to the hypotenuse.

Multiple Select

Which triangles are congruent?

• ∆TUS

• ∆RUT

• ∆SUT

• ∆RTS

Example:

• A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height of the roof.

• Step 1: Identify the similar triangles.

• Step 2: Set up proportions

Geometric Mean

Two positive numbers a and b is the positive number x that satisfies a/x=x/b. So x^2 = √ab

EX: Find the mean of 24 and 48.

x^2 = ab

x^2 = 24*48

x= √(24*48)

x=√24*24*2

x = 24√2

Multiple Choice

Find the value of the variable.

• 3√2

• √2

• 18

Fill in the Blanks

Find the value of each variable