Question

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?

Answer 1

1) Given

This matches a piece of given information.

2) `bar(RS) ~= bar(ST)`

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 `bar(RT)`

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

4) Transitive property of congruence

If `x~=y` and `y ~= z`, then `x~= 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.