Two polygons are congruent if and only if their corresponding parts are congruent.
In the definition, corresponding parts refer to corresponding angles and corresponding sides. Here we are given that two polygons are congruent.
BCDE≅ RSTU
The order of the vertices in the given congruence statement tells us which vertices correspond in the polygons. Let's use colors to illustrate this.
B C D E
≅
R S T U
Notice that on the diagram, there are two angles where the measure is expressed in terms of y. By the order of the vertices in the names of the polygons, we can tell that these are corresponding angles.
In congruent polygons, the corresponding angles are congruent, so they have the same measure. This allows us to set up an equation for y.
m∠D=m∠T ⇓
2y-31= y+11
Let's solve the equation using inverse operations.
