Chapter 12.5, Problem 28WE

To determine

To show:Every edge of $V-ABC$ is $k$ times as long as the corresponding edge of $V-XYZ$ .

Explanation of Solution

Given information:

The given expression is $VA=k\cdot VX$ .

Proof:

  $VA=k\cdot VX$ and both triangles are congruent.

  $\begin{array}{c}\frac{VA}{VX}=\frac{AB}{XY}\\ \frac{AB}{XY}=k\\ AB=kXY\end{array}$

The two triangles all other side will also in the same proportion so sides can be written in terms of their corresponding sides.

  $\begin{array}{c}\frac{AB}{XY}=\frac{AC}{XZ}\\ AC=kXZ\end{array}$

and,

  $\begin{array}{c}\frac{BC}{YZ}=\frac{AC}{XZ}=k\\ BC=kYZ\end{array}$

From the above, it is clear that every edge of $V-ABC$ is $k$ times as long as the corresponding edge of $V-XYZ$ .

Hence, proved.