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

https://lti.flvsgl.com/content/i52htqeb5l69atis2h76at8sb7/educator_geometry_v15_gs/module04/imgs/04_03c_26.jpg

Answer 2

@mathmale

Answer 3

What are your thoughts so far? What do "similar" and "congruent" mean? Which term applies here (not both, just one, of these terms applies).

Answer 4

similiar means kinda the same ... congruent means completely the same

Answer 5

@mathmale

Answer 6

In speaking of geometric shapes, "similar" implies that when you compare the 2 triangles, corresponding sides are proportional in length. I've checked and see that the hypotenuse of the larger triangle is 2x as long as the hypo. of the smaller triangle. Is that true when you compare the lengths of the longer legs of the 2 triangles?

This should help you decide whether to speak in terms of "similar" or of "congruent."

Answer 7

okay

Answer 8

yes that is true

Answer 9

We need to be precise in using these terms. "kinda the same" won't do; it's just not technical or accurate enough.

Here's what similar means under the circumstances:
The hypotenuse of the larger triangle is twice that of the smaller triangle.

Answer 10

okay but my geometry teacher is nice i dont think she will care what way as long as it makes seance

Answer 11

Also, the longer leg of the larger triangle is 2x that of the longer leg of the smaller triangle. Lastly, the shoter leg of the larger triangle is 2x that of the shorter leg of the smaller triangle.

This is a perfect example of SIMILAR TRIANGLES. Looking at any one side of one triangle, the corresponding side of the other triangle is a multiple of the first side.

Answer 12

i would say this is a totally congruent triangle

Answer 13

Actually, I'd not give your geom. teacher the benefit of the doubt and label her "nice" if she let you get away with defining "similar" as "kind of the same" in geometry.

Answer 14

can you explain what you mean by "I'd not give your geom. teacher the benefit of the doubt and label" i've always wondered what that means

Answer 15

Actually, you have 2 triangles and must discuss these 2 triangles together.
A single triangle can't be "congruent".
If the 2 triangles were of the same size and you could place one on top of the other for a perfect fit, then the 2 triangles would be "congruent." But in the given problem the 2 triangles are definitely not of the same size and thus could not possibly be congruent.

Answer 16

Glad to talk about the language I'm using here, but not until we get this geometry problem solved. It's all too easy to get distracted.

Answer 17

oh thats right silly me

Answer 18

they obviously cant be congruent idk why i thought that

Answer 19

If you were to use the pythagorean theorem in this problem, you could easily show that the length of the hypo. of the larger triangle is 2x the length of the hypo. of the smaller triangle.
It's even easier to show that the longer leg of the larger triangle is 2x the length of the longer leg of the smaller triangle.

And so on.
Because of these concrete facts, the two triangles are similar. Again, that means that all measurements of one triangle are PROPORTIONAL to the corresponding measurements in the other.

Answer 20

Repeat: the 2 triangles here are similar. They are not congruent.

Answer 21

yes i know

Answer 22

To understand what to do next, you might want to find the actual lengths of all 6 legs. I could help you get started: the length of the longer leg of the larger triangle is \[4\sqrt{2}\]

Answer 23

Can you convince yourself that this is true? I used the Pythagorean Theorem to find this result.

Answer 24

how do you know

Answer 25

idk how to find that if i dont have a set of points..