Geo 4.7 day 39.notebook
December 06, 2016
Warm Ups Day 39
2. Which pair of alternate interior angles are congruent?
B
1
A
5
2
6
3
C
4
D
4. Why are these triangles congruent?
E
G
D
F
Geo 4.7 day 39.notebook
December 06, 2016
HW 38 questions? Use a red pen to correct and complete. Name:
row#
SSS, SAS, ASA, ASA, HL proof wkst
1)
5
Geo 4.7 day 39.notebook
December 06, 2016
2)
statement
reason
Geo 4.7 day 39.notebook
3)
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statement
reason
Geo 4.7 day 39.notebook
4)
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statement
reason
Geo 4.7 day 39.notebook
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5)
statement
reason
Geo 4.7 day 39.notebook
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6) Given: AD BC , AB AC
ACD
Prove: ABD
A
B
D
C
statement
reason
Geo 4.7 day 39.notebook
December 06, 2016
7) Given: AB // DC, ÐD
ÐB
Prove: BAC
DCA
A
2
statement
reason
B
1
4
D
pass in
3
C
8) A parallelogram is a 4 sided figure where BOTH sets of opposite sides are parallel. Is ABCD a parallelogram? How can we be sure? Can we prove it?
Geo 4.7 day 39.notebook
Quick Quiz­ in pencil!
December 06, 2016
Geo 4.7 day 39.notebook
December 06, 2016
4­7 Triangle Congruence: CPCTC
GOAL
Use CPCTC to prove parts of triangles are congruent. Definition~1 total
CPCTC
Geo 4.7 day 39.notebook
December 06, 2016
Can you prove these triangles congruent? How?
statement
B
reason
C
A
F
D
E
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
Once you prove them congruent, you know all the rest of their parts are congruent. AC ÐA
ÐC
Geo 4.7 day 39.notebook
December 06, 2016
CPCTC can be used as a justification in a proof after you have proven two triangles congruent.
How you will use CPCTC in a proof
1) Prove the triangles are congruent using SSS, ASA, SAS, AAS, HL
SO YOU WILL NEED 3 THINGS!
2) Use CPCTC to prove that the other corresponding parts are congruent
THIS WILL GIVE YOU THE OTHER 3 THINGS!
Geo 4.7 day 39.notebook
December 06, 2016
Given: Ð A
ÐD
Ð DBC
Ð ABC
Prove: AC A
A
S
Using CPCTC
B
CD
Statement
Reason
<A = <D
given
<ABC = <CBD
given
BC = BC
Reflexive prop
∆ABC = ∆DBC
AAS
AC = CD
CPCTC
A
C
D
Geo 4.7 day 39.notebook
December 06, 2016
Example 1: Engineering Application
A and B are on the edges of a ravine. What is AB? Step 1) Are the triangles congruent? How?
Step 2) Use CPCTC to prove other corresponding
parts are also congruent.
Geo 4.7 day 39.notebook
December 06, 2016
A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK? Step 1) Are the triangles congruent? How?
Step 2) Use CPCTC to prove other corresponding
parts are also congruent.
Geo 4.7 day 39.notebook
December 06, 2016
1)
Statements
Reasons
Geo 4.7 day 39.notebook
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2)
Statements
Reasons
Geo 4.7 day 39.notebook
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3)
Statements
Reasons
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4)
MNOP is a parallelogram
Statements
Reasons
Geo 4.7 day 39.notebook
5)
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groups!
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6)
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7)
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Geo 4.7 day 39.notebook
December 06, 2016
HW 39: pg 271 4, 7 ­ 11, 17, 18, 19­21
and 4 proof cpctc wkst
From book problems, Copy down the given, what you are trying to prove, and the picture!
Remember, before you can use CPCTC, you must first prove triangles are CONGRUENT!
Geo 4.7 day 39.notebook
December 06, 2016