Question

If you're given that ΔJKL was dilated by a factor of 3/4 to create ΔWXY.

1.) Which triangle has a bigger area? How do you know? Make sure you justify your answer completely.

2.) If m∠K = 48o, and m∠L = 62o, what is the measure of ∠W?

Answer 1

Part 1) The original triangle ΔJKL has the bigger area

Part 2)
`m\angle W=70^o`

Explanation:

Part 1) Which triangle has a bigger area?

we know that

A dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

ΔJKL is similar to ΔWXY

The scale factor is 3/4

3/4 < 1

That means ---->The dilation is a reduction

therefore

The original triangle ΔJKL has the bigger area

Part 2) If m∠K = 48o, and m∠L = 62o, what is the measure of ∠W?

Remember that

If two figures are similar, then its corresponding angles are congruent

so

m∠J≅m∠W

m∠K≅m∠X

m∠L≅m∠Y

Find the measure of angle J

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

`m\angle J+m\angle K+m\angle L=180^o`

substitute the given values

`m\angle J+48^o+62^o=180^o`

`m\angle J=180^o-110^o=70^o`

therefore

`m\angle W=70^o`