Question

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

Answer 1

We already know that PQ and ST are congruent because they both equal 4 and QR and TU are congruent because they both equal 6. Also I'm not sure if it is marking the two angles congruent but it looks like that to me so if that is the case then both of the triangles are congruent by SAS, PQ=ST, WR=TU, angle PQR = angle STU.

Now that we need to set up a system of equations to find y. Since we already proved the triangles congruent SU must be = to PR because of CPCTC "corresponding parts of congruent triangles are congruent" So the equation would be:

3y-2=y+4 (move y variable to one side) subtract y from right, add 2 to right

2y=6 (divide)

y=3

Then plug 3 into where y is (and since we need PQR perimeter plug it into 3(3)-2) and PR should equal 7 so add up all the sides (4+6+7) and your perimeter is 17ft.