Chapter 7.3, Problem 1CE

To determine

To state: whether quadrilaterals ABCD, EFGH are similar or not

Answer to Problem 1CE

No, quadrilaterals ABCD, EFGH are not similar.

Explanation of Solution

  

In quadrilateral ABCD,

  $\begin{array}{l}AB=5\\ BC=5\\ CD=5\\ AD=5\end{array}$

In quadrilateral EFGH,

  $\begin{array}{l}EF=4\\ FG=2\\ GH=4\\ EH=2\end{array}$

Now take proportion of corresponding sides of quadrilaterals ABCD and EFGH.

  $\begin{array}{l}\frac{AB}{EF}=\frac{5}{4}\\ \frac{BC}{FG}=\frac{5}{2}\\ \frac{CD}{GH}=\frac{5}{4}\\ \frac{AD}{EH}=\frac{5}{2}\end{array}$

Clearly, the sides of quadrilaterals ABCD and EFGH are not proportional.

Use the fact: If corresponding sides of two quadrilaterals are not proportional then the two quadrilaterals are not similar.

So, ABCD and EFGH are not similar.