Chapter 6.3, Problem 12WE

To determine

To prove: that $\Delta RST$ is not equilateral.

Explanation of Solution

Given information:

  $\Delta RVT$ and $\Delta SVT$ are equilateral;

  $\Delta RVS$ is not equilateral.

Given figure,

  

Calculation:

An indirect proof is initiated by assuming temporarily that need to prove is untrue and then work from there to finally conclude that the assumption is untrue.

Proof:

Assume temporarily that $\Delta RST$ is equilateral.

If this is true, then $\Delta RVS$ should also be equilateral as three two triangles ashare a common base $RS$ and also since.

  $\overline{RV}=\overline{RT}=\overline{VT}=\overline{TS}=\overline{VS}$ .

However, this contradicts what is given that $\Delta RVS$ is not equilateral. Therefore our assumption that $\Delta RVS$ is not equilateral is not true.

Hence, it is proved that $\Delta RVS$ is not equilateral.