Question

Given JKLMN congruent to RSTUV, find MN if NJ=5x-10, UV=6x+3, and VR=3x-6.

Answer 1

Is there a graph/diagram or something to go along with the question?

Answer 2

No

Answer 3

I drew the graph for you.

Note that congruent means the two pentagons are exactly the same shape and size. This means that side MN is the same length as UV. And NJ is the same length as VR.

Answer 4

Would that make MN be 6x+3 ?

Answer 5

Solve for x first.

Answer 6

How?

Answer 7

Equate one side of the first pentagon to the equivalent side of the other pentagon. Then solve for x.

Answer 8

6x+3=6x+3?

Answer 9

MN= 6x+3 However you don't know what MN is yet. What other two sides can you make equal to each other? Remember they are the same length.

Answer 10

5x-10=6x+3=3x-6 ?

Answer 11

Close but you have taken three sides. Note this pentagon may not be a regular pentagon. Meaning not all of the sides are of equal length.

Answer 12

6x+3=3x-6?

Answer 13

The side in one pentagon has to be in the exact same position on the other pentagon. Again you are close, but those two sides are not in the exact same position

Answer 14

5x-10=3x-6

Answer 15

Bingo! Now solve for x.

Answer 16

x=2

Answer 17

Good now substitute the value for x into the other equation.

Answer 18

15

Answer 19

There you go. MN=15

Answer 20

Thank You

Answer 21

yw