Similar Right Triangles

Geometry

Chapter 9

A BowerPoint Presentation

Index card activity

Cut an index card diagonally.

Here is the shape you will have.

[You actually have TWO of these triangles. Save one of them for later!]

Index card activity

Draw an altitude from the right angle to the hypotenuse (you don’t need to use a protractor)

Index card activity

How many triangles do you see?

Index card activity

Cut along the altitude to split the big triangle into two smaller right triangles.

Index card activity

You now have three triangles (this is the time to use the other half of the index card, which is exactly like your original triangle).

What do you notice about these three triangles?

Index card activity

You now have three triangles (this is the time to use the other half of the index card, which is exactly like your original triangle).

What do you notice about these three triangles?

They are all SIMILAR to each other!

Parts of a right triangle

Parts of a right triangle

Here is an altitude from the right angle to the hypotenuse.

Parts of a right triangle

Here is an altitude from the right angle to the hypotenuse.

Parts of a right triangle

For our proportions, alt = altitude

and hyp = all of the hypotenuse

Parts of a right triangle

= part of the hypotenuse next to

= part of the hypotenuse next to

Altitude proportion

Leg 1 proportion

Leg 2 proportion

Summary of proportions

Solve for x

Does solving for x involve an altitude?

Solve for x

Yes – x is an altitude

Solve for x

Yes – x is an altitude

Solve for x

Yes – x is an altitude

Solve for x

Yes – x is an altitude

Solve for y

Does solving for y involve an altitude?

Solve for y

No – y is

Solve for y

y is

Solve for y

y is

Solve for y

y is

Solve for z

Does solving for z involve an altitude?

Solve for z

No – z is

Solve for z

z is

Solve for z

z is

Solve for z

z is