Two polygons are congruent if and only if their corresponding parts are congruent.
Here we are told that two triangles are congruent.
△L M N≅△Q R SThe 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 the vertices N and S.
L M≅Q R
Recall that congruent segments have equal measures. Therefore the two expressions given on the diagram must be equal. This observation allows us to set up an equation for x.
2x+11=3x-9
Now let's solve the equation using inverse operations.
