Part ll Day 5

Daily Objective- What are similar figures, and how do you find the missing lengths to them?
Objective Definition- Students will be able to define a similar figure and find missing lengths of them.

DEFINITION

Similar figure- Two geometrical objects are called similar if they both have the same shape.

WHAT DEFINES A SIMILAR SHAPE?

Example 1

These two triangles are similar. We can prove that they are similar using a ratio table to compare the lengths of their corresponding sides.

Big triangle	Small triangle
20	15
8	6
16	12

• In the table, you can see that the ratio of the bases is 15/20. This reduces to 43.
• Also in the table you can see that the ratio of the two right sides is 6/8. This reduces to 43.
• Finally, the ratio of the two left sides is 12/16. This reduces to 43.

Since all three ratios are equivalent, then the two triangles are similar.

2015=86=1612 Therefore, the two triangles are similar.

HOW TO FIND MISSING LENGTHS OF SIMILAR FIGURES?

Obtain the missing length if the given pair of triangles is similar.

Step 1

Label the vertices of the two similar triangles.

See the figure.

 

Step 2

The lengths of corresponding sides of similar figures are in proportion.

Here, the side AB corresponds to the side DE and the side BC corresponds to the side EF.

So,

Step 3

In a proportion, cross products are equal.

Write the cross products.

12 · 3 = x · 6

Step 4

Simplify both the sides. We get:

36 = 6x

Step 5

Here, x is multiplied by 6.

So, to isolate x, divide each side by 6.

Step 6

Simplify both the sides. We get:

6 = x

So, the length of the side DE is 6 in.

Step 6 of 6

Here's an awesome video explaining, check it out.

QUIZ TIME KIDS!

1.)Why are these two triangles similar  shapes?

2.) What is the height of the tree?

3.)What will x be.

ANSWER KEY!

1.)Because there given sides are proportional to each other. 8 is to 2 as 12 is to 3. And if you simplify both fractions 8/12 and 2/3 you get 2/3 which makes these proportional or similar shapes.

2.) 3=2 30=x(height of tree) 2/3 x/30. 2x30=60/3=20. The tree is 20 feet tall.

3.) x =....2/8 x/16...2x16/8=4. The answer is 4