Polygons and quadrilaterals

We are required to show that the pair of polygons is similar. We can do this by showing that the ratio of corresponding sides is equal and by showing that corresponding angles are equal.

We are given the angles. So, we can show that corresponding angles are equal.

All angles are given to be 90 ${}^{\circ }$ and

We first need to see which sides correspond. The rectangles have two equal long sides and two equal short sides. We need to compare the ratio of the long side lengths of the two different rectangles as well as the ratio of the short side lenghts.

Long sides, large rectangle values over small rectangle values:

Short sides, large rectangle values over small rectangle values:

The ratios of the corresponding sides are equal, 2 in this case.

Since corresponding angles are equal and the ratios of the corresponding sides are equal the polygons ABCD and EFGH are similar.

We are given that ABCDE and GHJKL are similar. This means that:

and

We are required to determine the

1. lengths $a$ , $b$ , $c$ and $d$ , and
2. angles $e$ , $f$ and $g$ .

The corresponding angles are equal, so no calculation is needed. We are given one pair of sides $DC$ and $KJ$ that correspond. $\frac{DC}{KJ}=\frac{4,5}{3}=1,5$ so we know that all sides of $KJHGL$ are 1,5 times smaller than $ABCDE$ .