Question

Could you check this for me?

Answer 1

Explain why the two figures below are not similar. Use complete sentences and provide evidence to support your explanation.

Answer 2

The reason they arent similar is because if you take side DE and JK the slopes are different which would make the angles different. Right?

Answer 3

or is there a different way to do it?

Answer 4

hint:
we have the subsequent ratios:
\[\frac{{CD}}{{IJ}} = \frac{3}{2},\quad \frac{{CB}}{{IH}} = \frac{{\sqrt 5 }}{{\sqrt 2 }}\]

Answer 5

for example, in order to compute the length of CB, I have applied the theorem of Pitagora. So I can write:
\[CB = \sqrt {{1^2} + {2^2}} = \sqrt {1 + 4} = \sqrt 5 \]
similarly for IH

Answer 6

Okay

Answer 7

as we can see those ratios are not equal each other, so, what can you conclude?

Answer 8

They are not similar

Answer 9

correct!

Answer 10

So instead of showing it as square root of 5 and 2 can i just show it as 2.2 and 1.4 then cross multiply?

Answer 11

because thats what i learned to do @Michele_Laino

Answer 12

What would be the ratio of CB and IH?

Answer 13

I think that, since the \(CB/IH\) ratio is expressed as irrational number, then it is better to write it like below:
\[\frac{{CB}}{{IH}} = \frac{{\sqrt 5 }}{{\sqrt 2 }} = \sqrt {\frac{5}{2}} \]

Answer 14

So if the ratio of CD and IJ are 3/2 and the ratio for CB and IH are √5/√2 how would you cross multiply that to see if it is similar or not

Answer 15

I understand, your question. We can consider another ratio in place of the ratio CB/IH

Answer 16

for example, we can consider these two ratios:
\[\frac{{CD}}{{IJ}} = \frac{3}{2},\quad \frac{{DF}}{{JL}} = \frac{4}{2}\]

Answer 17

Then cross multiply from that and you would get 6:8

Answer 18

So they wouldnt be similar..

Answer 19

more precisely, I can write this:
\[\frac{{CD}}{{IJ}} = \frac{3}{2},\quad \frac{{DF}}{{JL}} = \frac{4}{2} = 2\]
Now, since \(3/2 \neq 2\) then the two geometric shapes are not similar each other

Answer 20

Okay i see :)

Answer 21

ok! :)