Step by step
The question
Question: find AC.
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.
Angle A and angle D are both 60°: a pair of equal angles.
A for angle.
AB and DE are both 8: a pair of equal sides.
S for side.
Angle B and angle E are both 60°: a pair of equal angles.
A for angle.
2 Find the rule
AB is between the two angles: its letters are the two corners, A and B.
Go round: angle, side, angle: A S A.
The two angles fix the shape.
The side between them fixes the size.
There is only one way to draw it.
So A S A shows the triangles are congruent.
3 Use the matching parts
AC matches DF: A with D, C with F.
In congruent triangles, matching parts are equal.
So AC = DF.
So AC = 8.
Let's look back.
First: match the parts.
Then: find the rule.
Last: use the matching parts.