We are told that two triangles are congruent.
△ L M N≅△ Q R S
The order of the letters in the given congruence indicates corresponding vertices in the two triangles. Let's use colors to show this correspondence on the diagram. We can also use colors to indicate the corresponding sides.
Since the triangles are congruent, the corresponding sides are also congruent. Let's focus on the sides opposite to M and R.
L N≅Q S
Congruent segments have equal measure, so the two expressions given on the diagram must be equal.
This observation allows us to set up and solve an equation for x.
