Download Using Congruent Triangles: CPCTC

Using Congruent Triangles:
CPCTC
At the end of this lesson, you should
be able to use CPCTC to show that if
two triangles are congruent, then all
their corresponding sides and angles
are congruent.
Proving Congruent Triangles:




Recall, to prove
triangles congruent,
we used the following
postulates:
SSS
__________
SAS
__________
ASA
__________
AAS (SAA)
__________
AAA
ASS/SSA
CPCTC
CPCTC
stands for
Corresponding Parts of Congruent
Triangles are Congruent.
What does
CPCTC Mean?
It means that once we
know that two triangles
are congruent, we know
that all corresponding
(matching) sides and
angles are congruent!
Use
backwards
planning here!
Example
Think: If I can show that ∆ RAD ≡ ∆ AID,
then I can show any corresponding part
(side or angle) is congruent.
A
Statement Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
R
1 2
D
Given: RA ≡ AI; D
is the midpoint of
RI; ∠1 ≡ ∠2
Prove: ∠R ≡ ∠I
I
Use
backwards
planning here!
Think: If I can show that
∆ KON ≡ ∆ RON,
then I can show any corresponding part
(side or angle) is congruent.
Statement Reason
K
O
1
R
2
1.
1.
2.
2.
3.
3.
4.
4.
Given: ∠1 ≡ ∠2; ON
bisects ∠ KNR
5.
5.
Prove: ∠K ≡ ∠R
6.
6.
N
Checks for Understanding
1. What four ways do we
have two show that two
triangles are congruent?
2. For what does CPCTC
stand?
3. In your own words, what
does CPCTC mean?
4. Before using CPCTC, you
must always prove what
first?
Using CPCTC in Overlapping
Figures
Recall, a common 2-step method for
showing two segments or angles are
congruent is to:
Show ∆s congruent (SSS, SAS, ASA,
AAS)
Use CPCTC to show that the
corresponding parts (segments or angles
are congruent)
Is ∠ E ≡ ∠ R?
MN ≡ MA;
ME ≡ MR
E
N
M
E
Y
A
1. Label. 2. Color. 3. Redraw.
R
M
A
Showing Parts Congruent
∆ _____ ≡ ∆ ______
Reason: _______
(SSS, SAS, ASA, AAS)
All Corresponding
Angles Congruent
All Corresponding Sides
Congruent
∠ _____ ≡ ∠ _____
∠ _____ ≡ ∠ _____
∠ _____ ≡ ∠ _____
_____ ≡ _____
_____ ≡ _____
_____ ≡ _____
Reason: _______
Checks for Understanding
In your own words,
describe the
procedure for
showing segments
or angles in
overlapping figures
are congruent.
Homework:
CPCTC WS, plus text page 205: 7-14
all.
Weekly Quiz on Friday,
January 11, 2008 4.1- 4.4