Midsegments of a Triangle

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Midsegments of a Triangle
PowerPoint by J. Pavlicek (2005) Edited by J.
Stoops (2007)
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Objectives

• Identify the midsegments of a triangle
• Use properties of midsegments of a triangle

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Def A line segment whose endpoints are the
midpoint of two sides of a triangle is called a
midsegment of the triangle.
x
X
Y
2x
Theorem The segment connecting the midpoints of
two sides of the triangle is parallel to the
third side and half the length of the third side.
XY AB and XY (1/2) AB or AB 2(XY)
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Draw a ? ABC on a sheet of patty paper. Fold
and pinch to locate the three midpoints of the
triangle. Draw and label the three midpoints X,
Y, Z. Draw segments XY, YZ, and XZ.
X
Y
Z
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X
Y
Z
XY AB, XZ CB, and YZ AC
? AXZ ? ? XCY ? ? ZYB ? ? YZX
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Example
B (4, 6)
Y
A (-3, 5)
X
C (0, -2)
1.) Find the slope of midsegment XY. 2.) Find
XY. 3.) Find the slope of CB. 4.) Find CB.
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Example
X
Y
Z
1.) If the perimeter of ? CXY is 12 inches, what
is the perimeter of ? ABC?
2.) If the area of ? ABC is 36 sq. cm, what is
the area of ? AXZ?
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Example
B
?
F
( 3, 5)
?
(-3, 2)
A
?
G
?

• Find the coordinates of F,
• the midpoint of AB.
• Find the length of the median BE.
• 3. Find the length of the midsegment FG.

?
E
?
C
(4, -4)
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Let X, Y and Z be the midpoints of the sides of
?ABC.
Y
X
Z

• If XY 3x 12 and AB 8x 10, then XY ?
• If m?CBA 32o, then m?CYX ?
• Name one (1) triangle congruent to ?CXY.

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Assignment

• pg 290 12-19, 21-25, 28, 29 
• Review Sheet
• Chapter 5 Test Tuesday