Question

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

(b) What is the congruency that proves they are congruent?
(c) What is the perimeter of ∆PQR? Show ALL of your work.

Answer 1

Answer: a) Yes, triangles PQR and STU are congruent.

b) SAS congruence criteria

c) The perimeter of ∆PQR is 17 ft.

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`