Question

Which figure is similar to the parallelogram? (Figures may not be drawn to scale.) 689 8 5.8 58 112° 8 68° 6 4.8 4.8 112* 6 4.8 48 B?

Answer 1

We have to find the figure that is similar to the blue parallellogram.

For two figures to be similar they have to have the same shape (equal angle measures and proportional sides).

In this case, the rectangle at the bottom does not have the same shape (it has right angles) as the blue parallellogram. They are not similar.

The first option is a parallellogram that has the same angle measures but does not have proportional sides:

`\begin{gathered} (8)/(6)\approx1.33 \\ (5.8)/(4.8)\approx1.21 \end{gathered}`

The third option does not have the same angle measures (48º and 132º versus 68º and 112º), so they are not similar.

The fourth and last figure have the same angle measures, so we can check the proportionality of its sides to see if they are similar figures:

`\begin{gathered} (8)/(4)=2 \\ (5.8)/(2.9)=2 \end{gathered}`

Yes, they have the same scale factor (2), so the sides are proportional.

They are similar figures with the blue parallellogram.

Answer: Fourth option (same angle measures and proportional sides).