Homework - None Do Now 5/28/14 Mr. Adams has 15 sheets of construction paper for every 5 students. If Mr. Adams has 60 sheets of construction paper, how many students are in class? What is the unit rate? How many sheets of construction paper will Mr. Adams have if there are 24 students in class? Homework - None

Introduction What things in the classroom or at home have the same shape but not necessarily the same size?

Congruent Figures In order to be congruent, two figures must be the same size and same shape.

Similar Figures Similar figures must be the same shape, but their sizes may be different.

Similar Figures This is the symbol that means “similar.” These figures are the same shape but different sizes.

Proportional Sides Although the size of the two shapes can be different, the sizes of the two shapes must differ by a factor. 4 2 6 6 3 3 1 2

In this case, the “scale factor” is 2. Proportional Sides In this case, the “scale factor” is 2. 4 2 6 6 3 3 2 1

Enlargements – Scaled Up When you have a photograph enlarged, you make a similar photograph. X 3

Reductions – Scaled Down A photograph can also be made smaller to produce a slide. 4

Determine the length of the unknown side by using the “scale factor.” 15 12 ? 4 3 9

These triangles differ by a factor of 3. 15 3= 5 15 12 ? 4 3 9

Determine the length of the unknown side. ? 2 24 4

These dodecagons differ by a factor of 6. ? 2 x 6 = 12 2 24 4

Sometimes the factor between 2 figures is not obvious and some calculations are necessary. 15 12 8 10 18 12 ? =

To find this missing factor, divide 18 by 12. 15 12 8 10 18 12 ? =

The value of the missing factor is 1.5. 15 12 8 10 18 12 1.5 =

When changing the size of a figure, will the angles of the figure also change? 40 70 ? ? 70

Nope! Remember, the sum of all 3 angles in a triangle MUST add to 180 degrees. If the size of the angles were increased, the sum would exceed 180 degrees. 40 40 70 70 70 70

We can verify this fact by placing the smaller triangle inside the larger triangle. 40 40 70 70 70 70

The 40 degree angles are congruent. 70 70 70 70

The 70 degree angles are congruent. 40 40 70 70 70 70 70

The other 70 degree angles are congruent. 4 40 70 70 70 70 70

Find the length of the missing side. 50 ? 30 6 40 8

Let’s separate the two triangles. 50 ? 30 6 40 8

Now things are easier to see. 50 30 ? 6 40 8

The scale factor between these triangles is 5. 50 30 ? 6 40 8

The missing side length = 10 50 30 10 6 40 8

1) Determine the missing side of the triangle. ? 9 5 3 4 12

1) Determine the missing side of the triangle. 15 9 5 3 4 12

2) Determine the missing side of the triangle. 36 36 6 6 4 ?

2) Determine the missing side of the triangle. 36 36 6 6 4 24

3) Determine the missing sides of the triangle. 39 ? 33 ? 8 24

3) Determine the missing sides of the triangle. 39 13 33 11 8 24

Setting up Proportions http://www.youtube.com/watch?v=Joeq6K N2e-w A rectangle has dimensions 4ft by 14ft. Henry’s family is building a garden with the same shape as that rectangle. The shorter side of his garden will be 26 ft. How long will the longer side be?

Set up a Proportion A small rectangle is 3in by 5in. A similar rectangle has large side length 42in. What is the length of the shorter side?

Similarity is used to answer real life questions. Suppose that you wanted to find the height of this tree. Unfortunately all that you have is a tape measure, and you are too short to reach the top of the tree.

You can measure the length of the tree’s shadow. 10 feet

Then measure the length of your shadow. 10 feet 2 feet

If you know how tall you are, then you can determine how tall the tree is. 6 ft 10 feet 2 feet

The shapes formed by the shadows are similar triangles. x = 6 10 2 6 ft 10 feet 2 feet

Solve the proportion. The tree must be 30 ft tall. 10 feet 2 feet

Determine the height of the lighthouse. ? 8 2.5 10 Set up a proportion!

Determine the height of the lighthouse. 32 8 2.5 10

Determine the height of the car. ? 3 5 12 Set up a proportion!

Determine the height of the car. 7.2 3 5 12

Brain Pop Quiz http://www.brainpop.com/math/geo metryandmeasurement/similarfigur es/quiz/ Brooksidenj 123456

Homework None