Look at the corresponding congruent parts. Is there any postulate that you could use to show that △ ABE and △ CBD are congruent?
Practice makes perfect
We want to write a flow proof of the conjecture that triangles BE and BD 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:& ∠ A and ∠ C are right angles.
&∠ ABE ≅ ∠ CBD , AE ≅ CD
Prove:& BE ≅ BD
Since ∠ A and ∠ C are right angles, by definition they are congruent. Additionally, we are told that ∠ ABE ≅ ∠ CBD and AE ≅ CD. Let's highlight these two facts in the given diagram.
We can list what we know so far.
cc
∠ ABE ≅ ∠ CBD & Angle
∠ A ≅ ∠ C & Angle
AE ≅ CD & Non-included Side
By the Angle-Angle-Side (AAS) Congruence Postulate △ ABE and △ CBD are congruent.
△ ABE ≅ △ CBD
Recall that if two triangles are congruent, then their corresponding sides are also congruent. As a result, BE and its corresponding side BD are congruent.
Flow Proof
We can now summarize our findings in a flow proof.
