Question

Are these polygons similar or not . Figures ABCD and HIJK

Answer 1

Given the quadrilateral ABCD and the quadrilateral HIJK, you need to remember that, by definition, two figures are similar when their corresponding angles are equal and the length of their corresponding sides are proportional.

If the figures given in the exercise are similar, then this must be true:

`(AB)/(HI)=(BC)/(IJ)=(CD)/(JK)=(DA)/(KH)`

And this must be true too:

`\begin{gathered} m\angle A=m\angle H \\ m\angle B=m\angle I \\ m\angle C=m\angle J \\ m\angle D=m\angle K \end{gathered}`

You can identify that the angles markings shown in each figure indicate that the corresponding angles are congruent.

Now, in order to determine if the ratios of the lengths of their corresponding sides are equal, you can substitute values into the first equation:

`(AB)/(HI)=(BC)/(IJ)=(CD)/(JK)=(DA)/(KH)`

Knowing that:

You get:

Hence, the answer is: They are similar.