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1) Consider the Figure Below Part A: If PM=PN and

1) Consider the Figure Below Part A: If PM=PN and-example-1
User Robert Graves
by
2.6k points

1 Answer

14 votes
14 votes

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

User Sidhuko
by
2.3k points
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