Triangles ABC and DEF: AB = DE = 9, AC = DF = 7, angle B = angle E =…

Step by step, with the reason for every step · Congruent triangles · Geometry

Step by step

Question: which rule shows that triangles ABC and DEF are congruent?

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 9: a pair of equal sides.

S for side.

AB = DE = 9 S

AC and DF are both 7: a pair of equal sides.

S for side.

AC = DF = 7 S

Angle B and angle E are both 40°: a pair of equal angles.

A for angle.

angle B = angle E = 40° A

Angle B is not between the two sides: AC does not touch corner B.

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

AC → AB → angle B

Careful: S S A is not a rule.

Look: these two triangles have the same marked parts, but they are different.

SSA → not a rule

So we cannot tell if they are congruent.

There is no answer from these facts.

Let's look back.

First: match the parts.

Last: find the rule.

Answer

SSA → not a rule