CK-12 Geometry - Second Edition

5.1. Midsegments of a Triangle http://www.ck12.org

Solution:Find the midpoints ofABandBCusing your ruler. Label these pointsDandF. Connect them to create
the midsegment.

Don’t forget to put the tic marks, indicating thatDandFare midpoints,AD∼=DBandBF∼=FC.

Example 2:Find the midpoint ofACfrom 4 ABC. Label itEand find the other two midsegments of the triangle.

Solution:

For every triangle there are three midsegments.

Let’s transfer what we know about midpoints in the coordinate plane to midsegments in the coordinate plane. We
will need to use the midpoint formula,

(x 1 +x 2

2 ,

y 1 +y 2

2

)

.

Example 3:The vertices of 4 LMNareL( 4 , 5 ),M(− 2 ,− 7 )andN(− 8 , 3 ). Find the midpoints of all three sides,
label themO,PandQ. Then, graph the triangle, it’s midpoints and draw in the midsegments.

Solution:Use the midpoint formula 3 times to find all the midpoints.

LandM=

( 4 +(− 2 )

2 ,

5 +(− 7 )

2

)

= ( 1 ,− 1 ), pointO

LandN=

( 4 +(− 8 )

2 ,

5 + 3

2

)

= (− 2 , 4 ), pointQ

MandN=

(− 2 +(− 8 )

2 ,

− 7 + 3

2

)

= (− 5 ,− 2 ), pointP

The graph would look like the graph to the right. We will use this graph to explore the properties of midsegments.