Triangles ABC and DEF: AB = DE = 3, BC = EF = 4, angle B = angle E =…

Step by step

The question

Question: find DF.

Triangles ABC and DEF have the marked parts equal.

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: A with D, B with E, C with F.

DEF is turned over.

That does not matter.

AB and DE are both 3: a pair of equal sides.

S for side.

BC and EF are both 4: a pair of equal sides.

S for side.

Angle B and angle E are both 90°: a pair of equal angles.

A for angle.

2 Find the rule

Angle B is between the two sides: AB and BC both touch corner B.

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.

3 Use the matching parts

DF matches AC: D with A, F with C.

In congruent triangles, matching parts are equal.

So DF = AC.

So DF = 5.

Let's look back.

First: match the parts.

Then: find the rule.

Last: use the matching parts.