Question

What the pallelogram

Answer 1

see explanation

Explanation:

(1)

Corresponding angles are congruent, hence

∠W = ∠P = 80°

(2)

Ratios of corresponding sides are equal , that is

`(WZ)/(PS)` =
`(ZY)/(RS)` =
`(21)/(7)` = 3

multiply both sides by 5

WZ = 5 × 3 = 15

(3)

Similarly

`(WX)/(PQ)` =
`(ZY)/(RS)` = 3

`(WX)/(7)` = 3 ( multiply both sides by 7 )

WX = 7 × 3 = 21

(4)

The sides of WXYZ are each 3 times the size of PQRS

scale factor = 3

Answer 2

ANSWER


`1. \: m< \: W=80 \degree`


`2. WZ=15`


`3. WX = 21`


`4. \: k = 3`

EXPLANATION


Since WXYZ is a dilation of PQRS, the two shapes are similar.



The corresponding angles are equal.


Angle P corresponds to angle W.


This implies that,


`m< \: W=m< \: P=80 \degree`



2. Side SR corresponds to ZY.

We can observe that,


`|ZY|=21`



This implies that,



`|ZY|=3 * 7`



`|ZY|=3|SR|`


This implies that,


`WZ=3|SP|`



`WZ=3 * 5 = 15`



`3. WX = 21`

This side, XZ is parallel to ZY. The opposite parallel sides of a parallelogram are equal.




4. The scale factor is


`k= (image \: length)/(object \: length)`


`k= (21)/(7)`




`k= 3`


Therefore the scale factor is 3.