Part A )
Side Angle Side
Answer : C) SAS
Part B) :
For the given figure :
we have line PM ≅ PN,
Angle MPQ ≅ Angle NPQ
As in the triangle PMQ and triangle PNQ, the side PQ is common
Thus :
PM ≅ PN ( Given Side)
Angle MPQ ≅ Angle NPQ (given Angle)
PQ ≅ PQ ( Common Side )
Thus, by SAS Congurency, Triangle PMQ and Triangle PNQ is congurent.
Part C :
From the properties of congurent triangles :
The corresponding parts of congurent triangles are always equal.
In the congurent triangle PMQ and triangle PNQ
PM = PN, MQ = NQ, QP = QP
For the length PN:
In the given figure, we have PN = 11x +4 and PM = 17x - 8
as : PN = PM
11x + 4 = 17x - 8
Simplify for the x :
11x + 4 = 17x - 8
17x - 11x = 4 + 8
6x = 12
x = 12/6
x = 2
Substitute the value of x = 2 in the equation of the line PN
PN = 11x + 4
PN = 11(2) + 4
PN = 22 + 4
PN = 26
For the value of y :
as the side MQ = NQ
we have MQ = 3y - 7 and NQ = 41
So, MQ = NQ
3y - 7 = 41
3y = 41 + 7
3y = 48
y = 48/3
y = 16
Answer :
Part A : C SAS
Part C : PN = 26, y = 16