We want to write a flow proof of the conjecture that triangles JM and LM 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.
First, we know that angles J and L are congruent. Then, by the definition of an angle bisector, we have that ∠ JMK ≅ ∠ LMK. Let's include these facts in the diagram.
Notice that MK is a common side for both △ JMK and △ LMK. By the Reflexive Property of Congruent Segments we have that MK ≅ MK.
We can list what we know so far.
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∠ J ≅ ∠ L & Angle
∠ JMK ≅ ∠ LMK & Angle
MK ≅ MK & Non-included Side
By the Angle-Angle-Side (AAS) Congruence Postulate △ JMK and △ LMK are congruent.
△ JMK ≅ △ LMK
Recall that if two triangles are congruent, then their corresponding sides are also congruent. As a result, JM and its corresponding side LM are congruent.
Flow Proof
We can now summarize our findings in a flow proof.
