Triangles PQR and XYZ: PQ = XY = 4, angle Q = angle Y = 65, QR = YZ…

Step by step

The question

Question: which rule shows that triangles PQR and XYZ are congruent?

1 Match the parts

Congruent means the same shape and the same size.

One fits exactly on top of the other.

The order of the letters shows which corners match: P with X, Q with Y, R with Z.

XYZ is turned over.

That does not matter.

PQ and XY are both 4: a pair of equal sides.

S for side.

Angle Q and angle Y are both 65°: a pair of equal angles.

A for angle.

QR and YZ are both 9: a pair of equal sides.

S for side.

2 Find the rule

Angle Q is between the two sides: PQ and QR both touch corner Q.

Go round: side, angle, side: S A S.

Two sides and the angle between them fix the triangle.

There is only one way to draw it.

So S A S shows the triangles are congruent.

Let's look back.

First: match the parts.

Last: find the rule.