The Triangle Midsegment Theorem A segment whose endpoints ...

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The  Triangle  Midsegment  Theorem    

 

 

       

   

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The Midsegment of a Triangle A segment whose endpoints are the midpoints of two sides of a triangle. A

B

C

 

       

1. The midsegment is parallel to the third side of the triangle. 2. Its measure is equal one-half the length of the third side. A X is midpoint of AB X

Y

Y is midpoint of AC

B

C XY is a midsegment of ∆ABC XY ║ BC

     

XY =

1 BC 2

 

       

1. The midsegment is parallel to the third side of the triangle. 2. Its measure is equal one-half the length of the third side. A YZ is a midsegment of ∆ABC YZ ║ AB

1 YZ = AB 2

Y

B

Y is midpoint of AC

C

Z Z is midpoint of BC

 

           

1. The midsegment is parallel to the third side of the triangle. 2. Its measure is equal one-half the length of the third side. A

XZ is a midsegment of ∆ABC

X is midpoint of AB

XZ ║ AC

X

B

XZ =

1 AC 2

C

Z Z is midpoint of BC

     

 

© iTutoring.com The  Triangle  Midsegment  Theorem   Pg.  2  

       

XY, YZ, and XZ are midsegment of ∆ABC. If XY = 15, YZ = 8, and XZ = 12, find the perimeter of ∆ABC. A

15

X

Y 8

12 B

Z

C  

           

Solve for x and y 3x – 8 x + 12 2y – 6

y + 12

     

 

© iTutoring.com The  Triangle  Midsegment  Theorem   Pg.  3  

     

∆ABC are A(-4,-2), B(8,-4) and C(-2,6). Determine the coordinate of X, the midpoint of AB and Y, the midpoint of BC.

 

             

A segment whose endpoints are the midpoints of two sides of a triangle. 1. The midsegment is parallel to the third side of the triangle. 2. Its measure is equal one-half the length of the third side. A X is midpoint of AB X

Y

Y is midpoint of AC

B

C XY is a midsegment of ∆ABC XY ║ BC

   

XY =

1 BC 2

 

© iTutoring.com The  Triangle  Midsegment  Theorem   Pg.  4