Extra Credit Project

Similar Triangles in Everyday Situations

__________________________________________________________

Created by:

Carolina Jaramillo Period 1

Introduction

• Using proportions derived from similar triangles, I will find the height of the very top of my house.

HOW WILL I DO THIS ?

I will place a mirror on the floor between the object and me and look into it from a specific distance from

which I can view the top of the object clearly.The distances involved will be the make-up of the

proportions.

Heig

ht

of

house

Distance between object and mirror

Distance between mirror and me

My h

eig

ht

?

Why can I use these two triangles to set up a proportion?

• Knowing about similar triangles and their shortcuts, I could use the Angle-Angle-Similarity Theorem to make sure that these two triangles are similar.

•I know that <C and <O are congruent because they both are right angles and, believe it or not, ALL right angles are congruent.

•Also, I know that <FAC and <EAO are congruent because mirrors reflect off light at the same angle that light hits it.

•Therefore: ΔFCA ~ ΔEOA

O

E

F

AC

F

AO

E

C

Using the statement ΔFCA ~ ΔEOA, I will set up a proportion in which the corresponding sides will

be in place. I will use “x” in the proportion to denote the height of

my house.

My height corresponds to the house’s height. My distance from

the mirror corresponds to the house’s distance from the mirror.

My height = Me to mirror

House’s height House to mirror

Measuring Distances

I went outside and took my 2-foot ruler to begin my measuring...

mirror

me

ruler

notes

More measurements!

As I continued my measurements...

...my doggy slept!

ZZZZZZZZ...

...later, he woke up to watch me

What in the dog-world is she

measuring???

That project looks hard...

That’s too much math for

me...

Anyway…

getting back to the project…

♫ Plug it in, Plug it in ♫ …

My height = Me to mirror

House’s height House to mirror

57 = 31 x 264

Substitution

Now, cross-multiply and come up with a simple equation:

57(264) = 31(x)Simplify 15048 = 31x

485.4193548 = x

Division Prop. of equality

485 inches = x

Round

***Note: all measurements are in inches

• As you saw, I used a proportion to find the height of my house.

Height: About 485 inches

-or- about 40 feet

The End