Unit 7 Triangle Similarity

Dilations/ Similarity

100

What happens to an image when it is dilated by a negative scale factor

It flips upside down

200

Are they similar, if so, how?

No, sides are not proprtional

300

Triangle A has side lengths 4, 12 and 16

Triangle B has side lengths of 10, 30 and 40.

What is the scale factor from small to big and from big to small as fractions

5/2 and 2/5

400

There are 2 triangles are they similar if so How do you know

Triangle A has side lengths of 15.5 and 16.8 with and included angle of 78

Triangle B has side lengths 3.875 and 4.2 and an included angle of 19.5

No, if triangles are similar there side lengths are proportional while angles stay the same

500

Answer each of the following for 100points a piece

A/S/N

• A dilation preserves angle measures.

• A dilation preserves side lengths.

• If two triangles have one pair of congruent angles, they are similar.

• If two triangles have proportional sides, they are similar.  

• A dilation changes the shape of the triangle
  
  
  
  
  

A

S/N (scale factor of 1)

S

A

N

Triangle Similarity Theorems

100

The 3 similarity theorems for triangles.

AA, SSS, and SAS

200

How many letters are in the longest word in the dictionary

400 points closest without going over

45 Pneumonoultramicroscopicsilicovolcanoconiosis. 

300

If Triangle A has 2 angles measuring 74 and 59 degrees and Triangle B has 2 angles measuring 59 and 47 degrees. Are the 2 triangles similar Yes or No

Yes

400

For 2 triangles to be similar by SSS there ________________ side lengths must be _______________

corresponding

Proportional 

500

Are they similar, if so, how, by which thrm?

Yes, SAS

Proportions

100

In a triangle what is the relationship between midsegment and the side of the triangle parallel to it, give an example

The midsegment if half the length of the parallel side

Or

The parallel side is double the length of the midsegment

Midsegment=10, parallel side=20

200

Cross multiply the following 

x/4  =  16/x

x=8

300

What is x=2?

400

Solve for both x and y

x=4sqrt5

y=8sqrt5

500

Solve for a, b, and c.

a=6

b=6

c=4.5

Coordinate Plane Dilations and Proofs

100

When k>1 the dilation is an ___________________

When k<1 the dilation is a ________________

enlargement 

reduction

200

True or false

When a shape is dilated by a scale factor less than 1 the image is always inside the preimage

False

300

Steal another groups points if you get it correct 

Prove the following triangles are similar using any of the triangle similarity criterion Given Triangle ABC has coordinates A(4,4), B(8,4), C(10,8) and Triangle ADF has coordinates A(4,4), D(0,4), F(-2,-4)

Your choice

400

Dilate the point (4,5) with a scale factor of 3. With the center of dilation being (2,2). Give the coordinate of the new point

Where is (8,11)?

500

Dilate the triangle With coordinates A(3,3) B(0,1) C(5,-1) about the point (-1,-1) with a scale factor of 1/2 give the coordinates of the image

A'(1,1)

B'(-0.5,0)

C'(2,-1)

Challenges questions(1.5x)

100

If the Perimeter of a triangle is 32 and the scale factor is 2 whats the perimeter of the larger triangle

64

200

If the area of a triangle is 16, what is the area of a larger triangle is the scale factor is 2

64units ^2

300

See google docs for image with question answer as simplied radicals when necesary

12

4root(13)

6root(13)

400

Switch scores with another team if you get the question correct

Given the following image on Google Docs

NF=25

500

See google docs for image

Step 1: Solve for x  

Step 2: If the length of AB is the average of the AC and BC Find the length of EF

x=6

EF=12