Question

In the image below, a student designed two triangles for their coordinate cartoon drawing of a cat. The larger triangle was created to represent an ear and the smaller one was created to represent the cat’s nose. Are the two triangles shown similar? If so, what transformation was used to create the smaller triangle? If they are similar, what corresponding parts are congruent and which parts are proportional? If the triangles are not similar, explain why not. Make sure to provide evidence and explain your answer using complete sentences.

Answer 1

@ranga one more please, they're hard but you make them seem so easy

Answer 2

Calculate the length of each side of the triangle: AB, BC, AC and DE, DF, FE
I will calculate the first one: AB
To go from A to B I have to move 4 units along the x axis and 4 units along the y axis.
Therefore, AB = sqrt( 4^2 + 4^2 ) = sqrt( 16 + 16 ) = sqrt(32)
Use the same method to find other lengths.
Distance between two points = sqrt ( (x2-x1)^2 + (y2-y1)^2 ) =
sqrt ( (how much to move along x axis)^2 + (how much to move along y axis)^2 )

Answer 3

Could I try BC and you check if I got it?

Answer 4

Sure. For BC you can go from B to C or from C to B. Doesn't matter. The distance between B and C will be the same.

Answer 5

I didn't get it because the graph isn't numbered or labelled. Help?

Answer 6

Or could I just use any number

Answer 7

For finding distance between two points, all you need is the difference in the x coordinates and the difference in y coordinates between the two points. You don't need the absolute coordinates of each points. For finding the distance between A and B, I started from A and moved horizontally until I am directly below B and I counted the number of units I moved horizontally. Then I moved vertically and counted the number of squares moved to get to B. That is the difference in the y-coordinates.

Answer 8

Oh, right. Ok, What I got is: to move from C to B, I’d have to raise 6 units and run 2 units.

Answer 9

Correct. So the distance BC = sqrt( 6^2 + 2^2 ) = sqrt(36 + 4) = sqrt(40)

Answer 10

Ok, I'll try finding the rest.. one moment please

Answer 11

AC= sqrt (2^2 + 2^2) = sqrt (4 + 4) = sqrt (8)
DE= sqrt (2^2 + 2^2) = sqrt (4+4) = sqrt(8)
EF= sqrt (3^2 + 1^2) = sqrt(9+2)= sqrt(11)
FD= sqrt (1^2 + 1^2) = sqrt(1+1)= sqrt(2)

Ok, these're what I got..

Answer 12

So the triangles are not similar, right?

Answer 13

EF= sqrt (3^2 + 1^2) = sqrt(9+1)= sqrt(10)

Answer 14

I was just going to write that! lol, my bad

Answer 15

So the triangles are similar after all

Answer 16

For the left triangle, arrange the lengths from the highest to the lowest:
BC = sqrt(40), AB = sqrt(32), AC = sqrt(8)
Do the same for the triangle on the right. Arrange the lengths from the highest to the lowest:

Answer 17

AB= 32=8
BC=32=10
AC=8=2

Answer 18

You forgot the square roots.

Answer 19

AB= 8^2
BC= 10^2
AC= 2^2

Answer 20

BC = sqrt(40), AB = sqrt(32), AC = sqrt(8)
FE = sqrt(10), DE = sqrt(8), DF = sqrt(2)

Then take the ratio of the length of the corresponding sides and see if they are the same. If they are, then the triangles are similar.

BC / FE = sqrt(40) / sqrt(10) = sqrt(40/10) = sqrt(4) = 2
AB / DE = ?
AC / DF = ?

Answer 21

AB / DE = sqrt 4 =2
AC / DF = sqrt 4 =2

Answer 22

Therefore, triangles ABC and DEF are similar.
Notice the order of the letters in each triangle.
The first two letters are AB and DE and they are the corresponding sides.
Next two are BC and EF
The last is CA and FD