Use the definition of the midpoint. Is there a common side for both triangles?
Practice makes perfect
We want to write a flow proof of the conjecture that triangles MJK and MLK are congruent. Before we do that, let's recall what we know about flow proofs.
A flow proof uses statements written in boxes and arrows to show the logical progression of an argument. The reason justifying each statement is written below the box.
Let's begin by stating what we are given and what needs be the outcome of the proof.
Given:& MJ ≅ ML; K is the midpoint of JL
Prove:& △ MJK ≅ △ MLK
Recall that a midpoint divides a segment into two segments of the same length. As a result, we have that KJ ≅ KL. Let's include that in the diagram. We will also write the statement in a box.
We are told that sides MJ and ML are congruent. Since MK is common for both â–³ MJK and â–³ MLK, we have that all the three sides of â–³ MJK are congruent to their corresponding sides in â–³ MLK.
KJ &≅ KL
MJ &≅ ML
MK &≅ MK
By the Side-Side-Side (SSS) Congruence Postulate the triangles are congruent. We can now complete our flow proof.
