the midsegment theorem goal 1 using midsegments of triangles. goal 2 using properties of midsegments
TRANSCRIPT
The Midsegment Theorem
Goal 1 Using Midsegments of Triangles.
Goal 2 Using Properties of Midsegments.
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 half as long.
Using Midsegments of a Triangle
54
T
US
X
Y
Z
a) In XYZ, which segment is parallel to XY
b) Find YZ and XY
|| _____XY TU
_____YZ _____XY 8 10
Quick Check:
Find the m<VUZ.
ZY
U
X
V
65O
Identifying Parallel Segments• What are the three pairs of parallel segments in triangle
DEF?
• RS || ____• ST || ____• TR || ____
Example 1
DFEDFE
Example 2In the diagram, ST and TU are midsegments of
triangle PQR. Find PR and TU.
PR = ________ TU = ________16 ft 5 ft
Example 3In the diagram, XZ and ZY are midsegments of
triangle LMN. Find MN and ZY.
MN = ________ ZY = ________53 cm 14 cm
Finding Lengths• In triangle QRS,
• T, U, and B are midpoints.
• What are the lengths of TU, UB, and QR?
20TU
1(40)
2
1
2TU SR
25UB
1(50)
2
1
2UB QS
60QR
130 ( )
2QR
1
2TB QR
Example 4
Using Midsegments of a Triangle
10
6
KJ
LA
B
C
Find JK and AB
Example 5
JK = ________ AB = ________5 12
Example 6In the diagram, ED and DF are midsegments of
triangle ABC. Find the value of x and DF.
DF = ________26
3x- 4
52
x = ________10
Given: DE = x + 2; BC =
Find the value of x and DE.
D E
B C
A
18
x + 2
18
1
2DE BC
12 (18)
2x
2 9x
7x
9DE
Example 7
7
56
ST
RX
Z
Y
RTSTRS and,, are midsegments in XYZ. Find the perimeter of XYZ.
1210
14
12 10 14P
36P
Example 7
Given: X, Y, and Z are the midpoints of AB, BC, and AC respectively. AX = 2; XY = 3; BC = 9
Find the perimeter of ABC. (it’s a decimal)
Z
YX
A
B
C
3
62
922 92 6P
19P
Example 8
In XYZ, M, N and P are the midpoints.
The Perimeter of MNP is 64.
a) Find NP.
b) Find perimeter of XYZ
a) NP + MN + MP = 64 (Definition of Perimeter)
NP + + = 64 NP + = 64
NP =
b) P = XY + YZ + ZX
P = ___ + ___ + ____
P = ______
24
22
x
P
Y
M
N Z
5-1 Daily Quiz 12/1