5.1. Midsegments of a Triangle http://www.ck12.org
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 )Multi-Step ProblemThe midpoints of the sides of 4 RSTareG( 0 ,− 2 ),H( 9 , 1 ), andI( 6 ,− 5 ). Answer the following
questions.
- Find the slope ofGH,HI, andGI.
- Plot the three midpoints and connect them to form midsegment triangle, 4 GHI.
- Using the slopes, find the coordinates of the vertices of 4 RST.
- FindGHusing the distance formula. Then, find the length of the sides it is parallel to. What should happen?
More Coordinate GeometryGiven the midpoints of the sides of a triangle, find the vertices of the triangle. Refer
back to problems 19-21 for help.
- (-2, 1), (0, -1) and (-2, -3)
- (1, 4), (4, 1) and (2, 1)
Given the vertices of 4 ABC, find:
a) the midpoints ofM,NandOwhereMis the midpoint ofAB,Nis the midpoint ofBCandCis the midpoint ofAC.
b) Show that midsegmentsMN,NOandOMare parallel to sidesAC,ABandBCrespectively.
c) Show that midsegmentsMN,NOandOMare half the length of sidesAC,ABandBCrespectively.
25.A(− 3 , 5 ),B( 3 , 1 )andC(− 5 ,− 5 )
26.A(− 2 , 2 ),B( 4 , 4 )andC( 6 , 0 )For questions 27-30, 4 CAThas verticesC(x 1 ,y 1 ),A(x 2 ,y 2 )andT(x 3 ,y 3 ).