Chapter 6.5, Problem 11WE

To determine

To prove: $ST>SV$ in two column form.

Explanation of Solution

Given information:

Given figure,

  $\overline{TU}\cong \overline{US}\cong \overline{SV}$

Calculation:

Consider the following diagram:

The two columns proof is as follows:

Statements	Reasons
$m\angle STV<m\angle SUV$	Exterior angle inequality theorem $m\angle UST+m\angle STV=m\angle SUV$
$m\angle SVU>m\angle STV$	By Isosceles triangle theorem $m\angle SVU=m\angle STV$
$\overline{ST}>\overline{SV}$	Since, $\overline{SV}\cong \overline{SU}\cong \overline{TU}$Applying Side Angle Side Inequality.