Notice that QR is common for both △ TQR and △ SRQ.
Practice makes perfect
We want to write a flow proof of the conjecture that triangles TQR and SRQ 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 can begin by stating what we are given and what needs be the outcome of the proof.
Given:& △ TPQ ≅ △ SPR
& ∠ TQR ≅ ∠ SRQ
Prove:& △ TQR ≅ △ SRQ
We have that △ TPQ is congruent to △ SPR. If two polygons are congruent, their corresponding sides are also congruent. As a result, we have that QT≅ RS.
Let's now separate triangles TQR and SRQ into the figure below. We already know that sides QT and RS are congruent. We were also told that ∠ TQR ≅ ∠ SRQ. Let's highlight this fact in the diagram. Notice that side QR is common for both triangles.
We have that two sides and an included angle in triangle TQR are congruent to two sides and an included angle in triangle SRQ. By the Side-Angle-Side (SAS) Congruence Postulate, triangles TQR and SRQ are congruent.
△ TQR ≅ △ SRQ
We can now complete our flow proof.
