Corresponding sides and corresponding angles are the sides and angles that have the same relative positions in the different figures.
Corresponding Sides:
AB≅ CD
BG≅ DE
HG≅ FE
AH≅ CF Corresponding Angles:
∠ A≅ ∠ C
∠ B≅ ∠ D
∠ G≅ ∠ E
∠ H≅ ∠ F
Practice makes perfect
We were asked to identify all pairs of congruent corresponding parts in the given polygons. Corresponding sides and corresponding angles are the sides and angles that have the same relative positions in the different figures. We will first identify the sides and then the angles.
Congruent Sides
The naming convention in a congruence statement is very specific. Corresponding vertices have to be presented in the same order. However, we can write these statements in more than one way. Having been given that A B G H≅ C D E F, we already know which vertices are corresponding.
A corresponds to C
B corresponds to D
G corresponds to E
H corresponds to F
From here, we can identify congruent sides.
Let's summarize what we see in the diagram by writing the congruence statements.
AB ≅ CD
BG ≅ DE
GH ≅ EF
HA ≅ FC
Congruent Angles
To identify the corresponding angles, we can use the fact that the angles at corresponding vertices are corresponding angles.
Using what we know from the congruence statement, and by referring to our diagram, we can summarize the corresponding angles.
&∠ A≅ ∠ C
&∠ B≅ ∠ D
&∠ G≅ ∠ E
&∠ H≅ ∠ F
