Corresponding parts are the angles and sides that have the same relative positions in the different figures.
Corresponding Angles:
∠ G≅ ∠ Q
∠ H≅ ∠ R
∠ J≅ ∠ S
∠ K≅ ∠ T Corresponding Sides:
GH ≅ QR
HJ ≅ RS
JK ≅ ST
KG ≅ TQ Example Statement: HJKG≅ RSTQ
Practice makes perfect
Corresponding parts are the angles and sides that have the same relative positions in the different figures. We will first write another congruence statement and then identify the corresponding angles and sides.
Congruence Statement
The naming convention in a congruence statement is very specific. Corresponding vertices have to be presented in the same order. Having been given that G HJK≅ Q RST, we already know which vertices are corresponding.
G corresponds to Q
H corresponds to R
J corresponds to S
K corresponds to T
Therefore, the another possible congruence statement is HJK G≅ RST Q.
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.
& ∠ G≅ ∠ Q
& ∠ H≅ ∠ R
&∠ J≅ ∠ S
&∠ K≅ ∠ T
Congruent Sides
Since we already know the corresponding vertices, we can identify congruent sides.
Let's summarize what we see in the diagram.
G H &≅ Q R
HJ &≅ RS
JK &≅ ST
K G &≅ T Q
