Question

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100 POINTS

Which theorem/postulate can be used to prove ∆PQR ≅ ∆STU?
What is the perimeter of ∆PQR?

Answer 1

SSS

∆PQR = 43

Explanation:

The postulate to solve ∆PQR ≅ ∆STU is SSS. Both of the triangles have all three sides given, which means it can be solved for congruence.

9 + 6y + 5 + 14 = 9 + 8y +14

28 + 6y = 9 + 8y + 14

28 + 6y = 8y + 23

-6y -6y

--------------------------

28 = 2y + 23

-23 -23

---------------------

5 = 2y

---- ----

2 2

2.5 = y

9 + 14 + 6(2.5) + 5

23 + 15 + 5

23 + 20

43

∆PQR = 43

Answer 2

Solution given:

In ∆ PQR and ∆ STQ

PQ=ST=9ft given

<Q=<T given

QR=TU = 14ft [given]

S.A.S axiom therom is used to prove

∆PQR ≅ ∆STU

Since ∆PQR ≅ ∆STU

their corresponding side is equal.so

6y+5=8y

5=8y-6y

2y=5

y=5/2

now

perimeter of ∆ PQR=sum of all sides

=9ft +14ft+ 6*5/2+5=43ft