Answer: a) Yes, triangles PQR and STU are congruent.
b) SAS congruence criteria
c) The perimeter of ∆PQR is 17 ft.
Step-by-step explanation:
In the given picture, we can see in triangles PQR and STU
Segment PQ= Segment ST=4 ft
Segment QR= Segment TU=6 ft
∠ PQR=∠STU
Therefore, by SAS congruence criteria ,
Δ PQR ≅ ΔSTU
⇒ PR= SU [corresponding sides of congruent triangles are congruent]
[tex]\Rightarrow(3y-2)=(y+4)\\\Rightarrow\ 3y-2=y+4\\\Rightarrow\ 3y-y=4+2\\\Rightarrow\ 2y=6\\\Rightarrow\ y=3[/tex]
The perimeter of ∆PQR is given by :-
[tex]PQ+QR+PR=4+6+(3(3)-2)=10+(9-2)=10+7=17\ ft[/tex]
