Transcript Section 4.4 ~ Using CPCTC!

CPCTC
Be able to use CPCTC to find unknowns in congruent
triangles!
Are these triangles congruent?
By which postulate/theorem?
ΔLJK MNK
L
J
N
K
_____  _____
M
Oh, and what is the Reflexive Property again?
It says something is equal to itself. EX: A  A or AB  AB.
CPCTC
Once you have shown triangles are congruent, then you
can make some CONCLUSIONS about all of the
corresponding parts (_______
of
sides and __________)
angles
those triangles!
Corresponding Parts of
Congruent Triangles are
CONGRUENT!!
Are the triangles congruent? By which postulate or
theorem?
B
Y
Z
C
A
What other parts of
the triangles are
congruent by CPCTC?
B  Y
AB  ZY
BC  YX
X
Yes; ASA
If B = 3x and Y = 5x –9,
find x.
9
x
2
3x = 5x - 9
9 = 2x
Given:
1  2
C
3 4
L
SL  SR
Prove:
3  4
1
S
2
1.
Given
1. ___________
CS  CS
2. _______________
3.
2. Reflexive
SAS
3. ___________
3  4
4. _______________
CPCTC
4. ___________
R
Given:
Prove:
RC  HV
AR  EH
CA  VE
C
R  H
A
V
R
H
E
RC  HV ; AR  EH ; CA  VE 1. Given
1. _____________________
CRA  VHE
2. _____________________
2. SSS
R  H
CPCTC
3. _____________________
3. ________
State why the two triangles are congruent and write the
congruence statement. Also list the other pairs of parts that are
congruent by CPCTC.
R
C
Y  Q
Y Q
P
T
AAS
CT  RP
CY  RP
A geometry class is trying to find the distance across a small
lake. The distances they measured are shown in the
diagram. Explain how to use their measurements to find the
distance across the lake.
30 yd
40 yd
40 yd
24.5 yd
30 yd
Vertical angles are congruent.
The triangles are congruent by SAS.
The width of the lake has to be 24.5 yd by CPCTC.
A landscape architect sets up the triangles
shown in the figure to find the distance JK
across a pond. What is JK?
•One angle pair is congruent,
because they are vertical
angles.
•Two pairs of sides are congruent, because their
lengths are equal.
•Therefore the two triangles are congruent by SAS.
•By CPCTC, the third side pair is congruent, so JK =
41 ft.
Given: NO || MP, N  P
Prove: MN || OP
Statements
Reasons
1. N  P; NO || MP
1. Given
2. NOM  PMO
2. Alt. Int. s Thm.
3. MO  MO
3. Reflex. Prop. of 
4. ∆MNO  ∆OPM
4. AAS
5. NMO  POM
5. CPCTC
6. MN || OP
6. Conv. Of Alt. Int. s Thm.
Given: X is the midpoint of AC . 1  2
Prove: X is the midpoint of BD.
Statements
Reasons
1. X is mdpt. of AC. 1  2
1. Given
2. AX = CX
2. Def. of mdpt.
3. AX  CX
3. Def of 
4. AXD  CXB
4. Vert. s Thm.
5. ∆AXD  ∆CXB
5. ASA Steps 1, 4, 5
6. DX  BX
6. CPCTC
7. DX = BX
7. Def. of 
8. X is mdpt. of BD.
8. Def. of mdpt.