# A conjecture and the flowchart proof used to prove the conjecture are shown. Match the expression or phrase to each box to complete the proof?

Oct 18, 2016

1) Given

This matches a piece of given information.

2) $\overline{R S} \cong \overline{S T}$

A point on a line segment is a midpoint if and only if the line segments formed by that point and endpoints of the original line segment are congruent.

3) $S$ is the midpoint of $\overline{R T}$

This is our other piece of given information, and is necessary for the next step.

4) Transitive property of congruence

If $x \cong y$ and $y \cong z$, then $x \cong z$. This is known as the transitive property. It is best known as a property of equality, but also applies to congruence.

5) Definition of isosceles triangle

A triangle is called isosceles if two of its sides are congruent. We have shown this to be the case in the fourth item of the flowchart.