5.1. Midsegment Theorem http://www.ck12.org
Now that the points are plotted, find the slopes between all three.
slopeAB=^51 +−^24 =−^73
slopeBC=− 42 +− 51 =− 93 =−^13
slopeAC=^51 +−^15 =^46 =^23
Using the slope between two of the points and the third, plot the slope triangle on either side of the third point and
extend the line. Repeat this process for all three midpoints. For example, use the slope ofABwith pointC.
The green lines in the graph to the left represent the slope triangles of each midsegment. The three dotted lines
represent the sides of the triangle. Where they intersect are the vertices of the triangle (the blue points), which are
(-8, 8), (10, 2) and (-2, 6).
Practice
R,S,T,andUare midpoints of the sides of 4 X POand 4 Y PO.
- IfOP=12, findRSandT U.
- IfRS=8, findT U.
- IfRS= 2 x, andOP=20, findxandT U.
- IfOP= 4 xandRS= 6 x−8, findx.
- Is 4 X OP∼= 4 Y OP? Why or why not?
For questions 6-13, find the indicated variable(s). You may assume that all line segments within a triangle are
midsegments.
6.
7.
8.
9.
10.
11.
12.
13.- The sides of 4 XY Zare 26, 38, and 42. 4 ABCis formed by joining the midpoints of 4 XY Z.
a. Find the perimeter of 4 ABC.
b. Find the perimeter of 4 XY Z.
c. What is the relationship between the perimeter of a triangle and the perimeter of the triangle formed by
connecting its midpoints?
Coordinate GeometryGiven the vertices of 4 ABCbelow, find the midpoints of each side.
15.A( 5 ,− 2 ),B( 9 , 4 )andC(− 3 , 8 )
16.A(− 10 , 1 ),B( 4 , 11 )andC( 0 ,− 7 )
17.A( 0 , 5 ),B( 4 ,− 1 )andC(− 2 ,− 3 )
18.A( 2 , 4 ),B( 8 ,− 4 )andC( 2 ,− 4 )For questions 19-22, 4 CAThas verticesC(x 1 ,y 1 ),A(x 2 ,y 2 )andT(x 3 ,y 3 ).
- Find the midpoints of sidesCAandAT. Label themLandMrespectively.
- Find the slopes ofLMandCT.