Question

I need help with answering this please. I do not want the direct question, but how to obtain the correct answer. Thank you in advance.

Answer 1

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below:

Two rectangular tiles, rectangle PQRS with vertices at P(2, 2), Q(4, 2), R(4, 8), and S(2, 8). Rectangle JKLM with vertices J(5, 2) , K(6, 2), L(6, 5) and M(5, 5)

Which statement is correct?

A). The two tiles are not similar because segment SP is to segment SR is 5 : 1 and segment MJ is to segment ML is 2 : 3.

B.) The two tiles are similar because segment PQ is to segment QR is 1 : 3 and segment JK is to segment KL is also 1 : 3.

C.) The two tiles are similar because segment SR is to segment SP is 3 : 2 and segment ML is to segment MJ is also 3 : 2.

D.)The two tiles are not similar because segment PQ is to segment QR is 1 : 6 and segment JK is to segment KL is 1 : 3.

Answer 2

To know if two polygons are similar, you must do two things.
1. Each angle of the first polygon must be congruent to each corresponding angle of the second polygon.
2. All the ratios of the lengths each pair of corresponding sides are equal.

Answer 3

Do you understand the two conditions above?

Answer 4

Kind of.

Answer 5

Here is an example.

Answer 6

The example above uses triangles, but it's the same idea.
The question is: Are triangles ABC and DEF similar?

Answer 7

To answer we need to look at the angles and at the ratios of the lengths of the sides.

Answer 8

Yes, because they have the same shape and not the same size...Right?

Answer 9

Angles A and D are congruent.
Angles B and E are congruent.
Angles C and F are congruent.
So far the first condition is met. The three angles of one triangle are congruent to the three corresponding angles of the other triangle.

Answer 10

Okay.

Answer 11

Now let's look at the lengths of corresponding sides.
Here are the three pairs of corresponding sides.

AB and DE
BC and EF
AC and DF

Now we need to see if the ratios of lengths are the same.

Answer 12

That is what I am confused about...the ratio part of the question.

Answer 13

Ratios of lengths of corresponding sides:

AB to DE = \(\dfrac{1}{3}\)

BC to EF = \(\dfrac{\sqrt 3}{3 \sqrt 3} = \dfrac{1}{3}\)

AC to DF = \(\dfrac{2}{6} = \dfrac{1}{3} \)

Answer 14

You see how every side of triangle ABC is 1/3 the length of the corresponding side of triangle DEF?

Answer 15

That is what equal ratios of the lengths of corresponding sides means.

Answer 16

Yes. But how do I get that with my question? How do I solve to find the ratio with coordinates?

Answer 17

Now we need to apply this same method to your two polygons.

Answer 18

Remember the 2 steps for similarity of polygons.
1. congruent corresponding angles
2. equal ratios of corresponding side lengths

Answer 19

Let's look at the angles of the two polygons.
Can you tell what angles these two quadrilaterals have?

Answer 20

For example, look at points P and S.
Do you see that the both have x-coordinate 2?
What does that tell you about segment PS?

Answer 21

The ratio is 2? (I am really bad at this, I apologize)