3.1 Test Review Dilation and Similar Triangles

Dilation and Similar Triangles Review

The test is approaching soon....

Multiple Select

Which of the following Criterion can be used to prove two triangles are similar to eachother?

• AA

• SAS

• SSS

• SS

• SSA

In the example, since ΔABC has two angles that are congruent to two corresponding angles of ΔDEF, we know the two triangles are similar by AA.

​AA

In the example, both triangles have an angle of 50⁰, to prove they are congruent by SAS we have to show that the corresponding sides are proportional. Setting up the proportion and reducing the fractions we have enough information to say that ΔABC~ΔDFE

SAS

In the example we want to show the two triangles are proportional by SSS, so we have to show that the corresponding sides are proportional.
I started by setting up my proportion (demonstrated in blue, green, and purple). I then reduced each fraction.
Since 2 does not equal 5/3, that means these two triangles are NOT similar.

SSS

Multiple Choice

Are the triangles similar?

• Yes by AA

• Yes by SAS

• Yes by SSS

• No

Multiple Choice

Are the following two triangles similar?

• Yes by AA

• Yes by SAS

• Yes by SSS

• No the sides are not proportional

Multiple Choice

Are the following two triangles similar?

• Yes by AA

• Yes by SAS

• Yes by SSS

• No the sides are not proportional

​The two triangles are similar. One way to write this out would be ΔLGE~ΔMRA
The symbol "~" means similar and may look familiar because it's part of the symbol for congruence ≅

The order we write LGE and MRA matters, we want the letters to correspond. Angle G and Angle R are both the same angle so they are both in the middle. Angle E and Angle A are also the same angle and they are both at the end.

Fill in the Blanks

​A common mistake I see with these types of problems is some like to put 40 and 56 together, but they are not corresponding sides. The corresponding side to 40 is x.

Math Response

Solve for x.

Type answer here

Correct Answer: 45

Deg^°

Rad

​When presented a problem with two triangles the best option is to split them up and relabel them like I did in red and blue. Keep in mind the length of HM is 32, but its split in the original image, this is a common mistake people make.
Once you have two separate triangles the problem becomes easy, set up your proportion and cross multiply.

Math Response

Solve for x. DO NOT round your answer.

Type answer here

Correct Answer: 47.5

Deg^°

Rad

Dilation of a point

Fill in the Blanks

​To find out what the scale factor or a shape is we have to do just a few things.
First we have to recognize which shape is the original or "old" and which one is knew. In the shapes on the left the old shape is labeled with A, B, C, and D while the new shape is A', B', C', and D'.
Now that we know which one is old and new we can find the scale factor.

​Once you've identified the new and old shape you can compare the points or the side lengths to get the scale factor as demonstrated below.

Math Response

In the dilation pictured, what is the scale factor?

Type answer here

Correct Answer: \frac{1}{3}

Deg^°

Rad

​Say we need to find the perimeter of the smaller triangle. In order to do this we must first find the missing sides. I labeled them as x and y then found them individually so I could add the three sides together as demonstrated below.

Math Response

Find the perimeter of the smaller triangle.

Type answer here

Correct Answer: 40

Deg^°

Rad

Math Response

A tree is cut down and it's stump has a surface area of 27 $$in^2$$ . An artist draws the stump at 2/3 its original size on sketch paper. What is the area of the stump on the sketch?

Type answer here

Correct Answer: 12

Deg^°

Rad

Math Response

A shape has an area of 6 $$in^2$$ . The shape enters a super soldier serum chamber and grows with a scale factor of 3. What is the area of the shape now?

Type answer here

Correct Answer: 54

Deg^°

Rad

You know your height is exactly 6 foot tall and you cast a shadow that is 8 foot long. The mountain casts a shadow that is 1944 feet long, so how tall is the mountain?

​This is a visual representation of the problem, the next slide shows it in a more mathy look.

You know your height is exactly 6 foot tall and you cast a shadow that is 8 foot long. The mountain casts a shadow that is 1944 feet long, so how tall is the mountain?

Math Response

You are exactly 6ft tall and you cast a shadow that is 8ft long. A flag pole next to you casts a shadow that is 32ft long, how tall is the pole?

Type answer here

Correct Answer: 24

Deg^°

Rad

​Angle Splitter Theorem: When you bisect an angle in a triangle, the line creates a proportion with the sides as demonstrated.

Math Response

Solve for x.

Type answer here

Correct Answer: 8

Deg^°

Rad

​Side Splitter Theorem: A line that is parallel to a side of the triangle and splits the other two sides of the triangle creates a proportion as shown.

Multiple Choice

Which proportion is justified by the image?

• $$\frac{6}{8}=\frac{4}{3}$$

• $$\frac{6}{8}=\frac{3}{4}$$

• $$\frac{6}{14}=\frac{4}{3}$$

• $$\frac{6}{14}=\frac{3}{4}$$