Question

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

Answer 1

check the picture below

Answer 2

The two figures below are not similar

Explanation:

we know that

If the two figures are similar

then

the ratio of their corresponding sides are equal

`(CD)/(IJ)=(DE)/(JK)`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Step 1

Find the distance CD

`C(-4,2)\\D(-1,2)`

substitute the values

`d=\sqrt{(2-2)^(2)+(-1+4)^(2)}`

`d=\sqrt{(0)^(2)+(3)^(2)}`

`dCD=3\ units`

Step 2

Find the distance IJ

`I(2,1)\\J(4,1)`

substitute the values

`d=\sqrt{(1-1)^(2)+(4-2)^(2)}`

`d=\sqrt{(0)^(2)+(2)^(2)}`

`dIJ=2\ units`

Step 3

Find the distance DE

`D(-1,2)\\E(0,0)`

substitute the values

`d=\sqrt{(0-2)^(2)+(0+1)^(2)}`

`d=\sqrt{(-2)^(2)+(1)^(2)}`

`dED=√(5)\ units`

Step 4

Find the distance JK

`J(4,1)\\K(5,0)`

substitute the values

`d=\sqrt{(0-1)^(2)+(5-4)^(2)}`

`d=\sqrt{(-1)^(2)+(1)^(2)}`

`dJK=√(2)\ units`

Step 5

Find the ratios of the corresponding sides

Remember that

If the figures are similar

then

the ratio of their corresponding sides are equal

`(CD)/(IJ)=(DE)/(JK)`

we have

`dCD=3\ units`

`dIJ=2\ units`

`dED=√(5)\ units`

`dJK=√(2)\ units`

Substitute

`(3)/(2)\\eq (√(5))/(√(2))`

therefore

the figures are not similar