Question

3. (a) Are triangles PQR and STU congruent?

Answer 1

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]

$\Rightarrow(3y-2)=(y+4)\\\Rightarrow\ 3y-2=y+4\\\Rightarrow\ 3y-y=4+2\\\Rightarrow\ 2y=6\\\Rightarrow\ y=3$

The perimeter of ∆PQR is given by :-

$PQ+QR+PR=4+6+(3(3)-2)=10+(9-2)=10+7=17\ ft$