Transcript 3.7 Midsegments of Triangles & Trapezoids

Warm up
3.7 Midsegments of
Triangles & Trapezoids
FYI
3.7 today
3.8 next time
Review the time after that...
Then… Chapter 3 test the time after that
Midsegment of a triangle
• A segment whose endpoints are the
midpoints of two sides. It is parallel to
one side of the triangle and its measure is
½ of that side.
If AE = 15
C
midsegment
B
½X
D
Find the
measure of
BD
BD = 7.5
A
E
X
TRY THIS
3X - 5
A
3X – 5 = 2(X + 2)
E
X+2
B
3X – 5 = 2X + 4
X=9
D
AE = 22 units
BD = 11
C
X2 + 1 = 2 (X)
AND THIS
X2 – 2X + 1 = 0
C
(X – 1) (X – 1) = 0
B
X
D
X=1
BD = 1 units
AE = 2 units
A
E
X2 + 1
Midsegment of a Trapezoid
♥ A segment whose endpoints are the midpoints of
the NON-PARALLEL sides.
♥ It’s parallel to the bases and
♥ its measure = (Sum of the bases)
2
BASES
Midsegment
Try this
X
A
B
C
Find the lengths of the
parallel segments
when x = 2
AM = 2
M
BY = 7
X+5
CZ = 12
Y
?
Z
Find ?
? = X + 10
Check to make sure
these numbers work…
2 + 12 = 7
2
YEA!!
Try this…
If AZ = 25 and
CX = 31, find BY
BY = 28
C
B
A
X
and this…
If AZ = x2 + 4x - 36
and
Y
Z
CX = x2 + 2x - 40
and BY = 16
Find the lengths of
the bases
Uno mas
Find the lengths of BD and AE if
BD = 4x – 4 and AE = 10x – 12
2(4x-4) = 10x – 12
8x – 8 = 10x -12
4 = 2x
C
X=2
B
D
BD = 4
A
E
AE = 8
Assignment
Pg 186, 5-8, 10-16, 22, 28-30, 32-40