Question

cool down
lesson 4: scaled relationships
cool down: corresponding polygons
here are two polygons on a grid.
is pqrst a scaled copy of abcde? explain your reasoning.

Explanation:

Step1: Check side - length ratios

Count grid units for corresponding sides. For example, side $AB$ has a vertical length of 3 units and side $PQ$ has a vertical length of 6 units. The ratio of the vertical length of $PQ$ to $AB$ is $\frac{6}{3}=2$. Side $BC$ has a horizontal length of 1 unit and side $QR$ has a horizontal length of 2 units, ratio $\frac{2}{1} = 2$.

Step2: Check all corresponding sides

Check all other corresponding sides in the same way. For the slanted sides, using the Pythagorean theorem (if needed). For the slanted side of $AE$ and $PT$, the rise - over - run relationship also shows a ratio of 2. Since the ratio of all corresponding side lengths of $PQRS$T to $ABCDE$ is 2, and the angles remain the same (because of the grid - based structure and similar shape), $PQRS$T is a scaled copy of $ABCDE$.

Answer:

Yes, $PQRS$T is a scaled copy of $ABCDE$ because the ratio of all corresponding side lengths is 2 and the angles are congruent.