Step by step
The question
Question: which rule shows that triangles ABC and DEF 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: A with D, B with E, C with F.
DEF is turned over.
That does not matter.
Angle B and angle E are both 90°: a pair of equal angles.
A for angle.
angle B = angle E = 90° A
AB and DE are both 5: a pair of equal sides.
S for side.
AB = DE = 5 S
BC and EF are both 12: a pair of equal sides.
S for side.
BC = EF = 12 S
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.
AB → angle B → BC
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.
SAS → congruent
Let's look back.
First: match the parts.
Last: find the rule.
Answer
SAS → congruent