Prove triangles PQR and XYZ are congruent: PQ = XY, angle Q = angle…

Step by step

The question

Question: prove that triangles PQR and XYZ are congruent, then that PR = XZ.

We know: PQ = XY, ∠Q = ∠Y, QR = YZ.

We must show why △PQR ≅ △XYZ and PR = XZ.

Careful!

The letters go in the same order: the first letters match, the second letters match, and so on.

A proof is a table.

On the left: what we know.

On the right: why it is true.

1 Write what we know

First, what we are told.

PQ = XY

Also given: ∠Q = ∠Y

Also given: QR = YZ

2 Reach the goal

Two sides and the angle between them: side, angle, side.

△PQR ≅ △XYZ

PR and XZ are in the same place in the two triangles.

PR = XZ

3 Check

Let's check: every row has a reason.

And the last row is what we had to prove: PR = XZ.

The proof is done!

Let's look back.

First: write what we know.

Then: reach the goal.

Last: check.