1. Geom3­4Final.notebook October 13, 2011
BELL WORK Given: 7 = 8 7 Z Y
ZY = WX 9
Prove: W = Y
Don't give up on this one!
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Do what you can. W X 8
(ultimately you want to get to CPCTC)
Agenda for today:
• turn in p.120/127 and packet
• 3.4 ­ beyond CPCTC!
• receive review packet for 3.1­3.4 test
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2. Geom3­4Final.notebook October 13, 2011
3.4 ­ Beyond CPCTC
After this class, you should be able to :
• define and construct medians, altitudes, and auxiliary lines.
• write proofs involving steps beyond CPCTC.
A median of a triangle is a line segment drawn from any
vertex of a triangle to the midpoint of the opposite side.
Let's use medians in a proof:
S
Given: T = Y
SVZ = SXZ
TV = YX
Conclusion: SZ is the median to TY
V X
T Z Y
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3. Geom3­4Final.notebook October 13, 2011
Altitude of a triangle:
Definition?
Lets use altitudes in a proof: A
Given: CD and BE are altitudes of ABC
AD = AE
Prove: DB = EC D E
B C
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4. Geom3­4Final.notebook October 13, 2011
Sometimes proofs would be easier if the A
diagram looked different. Let's do an example:
Given: AB = AC
BD = CD
Conclusion: ABD = ACD
D
B C
auxiliary lines ­ additions that WE make to the diagram
We can do this because two points determine a line.
Now back to our proof.
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5. Geom3­4Final.notebook October 13, 2011
1. median
2. altitude
3. auxiliary line
BELL WORK:
Draw WRT.
Then construct the altitude from vertex W to RT.
W
R T
Homework: Review packet for test 3.1­3.4
Due Friday.
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