Download 5-1 PPT Triangle Midsegments

Section 5-1 Triangle Midsegments
SPI 32J: identify the appropriate segment of a triangle given a
diagram and vs (median, altitude, angle and perpendicular bisector)
Objectives:
• Use properties of midsegment to solve problems
Do Investigation
On page 243
Line segment LN is the midsegment of the triangle
(connects the midpoint of the two sides)
LN = ½ AB
Triangle Midpoint Theorem
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle,
then the segment is parallel to the third side and is ½ its
length.
Length of Midsegment = ½ length of base
Finding Lengths using Triangle Midpoint Theorem
In ∆ XYZ, M, N, and P are midpoints.
The perimeter of ∆ MNP is 60. Find
NP and YZ.
Because the perimeter of MNP is 60, you can find NP.
NP + MN + MP = 60
Definition of perimeter
NP + 24 + 22 = 60
Substitute 24 for MN and 22 for MP.
NP + 46 = 60
Simplify.
NP = 14
Subtract 46 from each side.
Use the Triangle Midsegment Theorem to find YZ.
MP = 1 YZ
2
22 = 1 YZ
2
44 = YZ
Triangle Midsegment Theorem
Substitute 22 for MP.
Multiply each side by 2.
Apply Midpoint Theorem
Find m AMN and m ANM.
MN and BC are cut by transversal AB , so
B are corresponding angles.
AMN and
MN || BC by the Triangle Midsegment Theorem, so
AMN
B because parallel lines cut by a transversal
form congruent corresponding angles.
m AMN = 75 because congruent angles have the
same measure.
In AMN, AM = AN, so m
Triangle Theorem.
m
ANM = m
ANM = 75 by substituting 75 for m
AMN by the Isosceles
AMN.
Real World: Apply Midpoint Theorem
Indirect Measurement. Kate wants to paddle
her canoe across the lake. To determine how
far she must paddle, she paced out a triangle
counting the number of strides as shown.
a. If Kate’s strides average 3.5 ft, what is the length of the
longest side of the triangle?
b. What distance must Kate paddle across the lake?
a. 1050 ft
b. 437.5 ft