We want to write a flow proof of the conjecture that triangles JML and MJK 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.
We begin by stating what we are given and what needs be the outcome of the proof.
Given:& JK ∥ LM, JL ∥ KM
Prove:& △ JML ≅ △ MJK
Let's now take a look at the diagram. Notice that JM is a transversal to the parallel segments JK and LM. It is also a transversal to the parallel segments JL and KM.
By applying the Alternate Interior Angles Theorem we get that the two following pairs of angles are congruent.
∠ KJM ≅ ∠ JML
∠ JMK ≅ ∠ LJM
Also notice that JM is a common side for both triangles. By the Reflexive Property of Congruent Segments it is congruent to itself. Let's summarize our findings.
cc
∠ KJM ≅ ∠ JML & Angle
JM ≅ JM & Included Side
∠ JMK ≅ ∠ LJM & Angle
Consequently, by applying the Angle-Side-Angle (ASA) Congruence Postulate we can conclude that △ JML and △ MJK are congruent. Let's summarize this proof using a flow chart.
