Math  /  Geometry

QuestionAre these shapes similar? yes no
Work it out Not feeling ready yet? These can help: Submit Similarity statements Identify equivalent ratios Lesson: Similarity Ready to go back? Return to your original skill

Studdy Solution

STEP 1

What is this asking? Do the side lengths of these two rectangles form the same ratios? Watch out! Corresponding sides need to be compared to check for similarity, not just any two sides!

STEP 2

1. Set up ratios
2. Compare ratios

STEP 3

Alright, let's **dive in**!
We're going to compare the ratios of corresponding sides.
What does that even mean?
It means we match up the sides that are in the same position on each rectangle.
Think of it like matching socks – you want the stripes with the stripes, the polka dots with the polka dots!

STEP 4

In our rectangles, MNMN matches with UVUV, and NONO matches with UTUT.
So, let's write those ratios!
Our first ratio is MNUV\frac{MN}{UV}, which is 2542\frac{25}{42}.
Our second ratio is NOUT\frac{NO}{UT}, which is 3425\frac{34}{25}.

STEP 5

Now for the **moment of truth**: are these ratios equal?
Let's see!
We have 2542\frac{25}{42} and 3425\frac{34}{25}.
If these rectangles were similar, these fractions would be equal.

STEP 6

One way to check is to cross-multiply.
If we multiply 252525 \cdot 25, we get 625625.
If we multiply 423442 \cdot 34, we get 14281428.
Since 625625 is *definitely* not equal to 14281428, we know the ratios aren't equal!

STEP 7

Another way to think about it is to simplify the fractions. 2542\frac{25}{42} is already simplified, but 3425\frac{34}{25} is also simplified!
Since they don't look the same, they aren't the same!

STEP 8

The ratios of corresponding sides are not equal, so the rectangles are *not* similar.
The answer is no!

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