Questions: Quadrilateral XGLD can be mapped onto quadrilateral IMEW by a rotation. If LD=22, find EW.

Transcript text: Quadrilateral $X G L D$ can be mapped onto quadrilateral $I M E W$ by a rotation. If $L D=22$, find $E W$.

Solution

Solution Steps

To solve this problem, we need to understand that a rotation is a rigid transformation, meaning it preserves the lengths of the sides of the quadrilateral. Therefore, the length of side $LD$ in quadrilateral $XGLD$ will be equal to the length of side $EW$ in quadrilateral $IMEW$.

Solution Approach

Since a rotation preserves the lengths of the sides, we can directly assign the length of $LD$ to $EW$.

Step 1: Understanding the Problem

We are given two quadrilaterals, $XGLD$ and $IMEW$, which can be mapped onto each other by a rotation. A key property of rotations is that they preserve the lengths of corresponding sides.

Step 2: Identifying Corresponding Sides

From the problem, we know that the length of side $LD$ in quadrilateral $XGLD$ is given as $LD = 22$. Since the quadrilaterals are related by a rotation, the length of the corresponding side $EW$ in quadrilateral $IMEW$ must also be equal to $LD$.

Step 3: Conclusion

Thus, we can conclude that the length of side $EW$ is equal to $22$.