Chapter 14.1, Problem 13WE

To determine

To find: The way of mapping each point of $\overline{DC}$ to a point of $\overline{AB}$ so that the mapping is one-to-one mapping and check whether the mapping is isometry or not.

Answer to Problem 13WE

The mapping is one-to-one mapping and it is not isometry.

Explanation of Solution

Given information:

It is given that $ABCD$ is trapezoid.

  

Calculation:

It is given that $ABCD$ is trapezoid and each point of $DC$ is mapped by using similar parallel measurements to the side $AD$ .Then the mapping is one-to-one mapping.

No, the mapping will not be isometry because the distance between the pre images, $A\text{and}B$ is larger than the distance between their corresponding images, $D\text{and}C$ .

Therefore, the mapping is one-to-one mapping and it is not isometry.