cpctc - wikispaces6.4.pdf/... · marcel is painting the triangular section of a shuffleboard court...
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CPCTCCorresponding Parts of Congruent Triangles are Congruent
Quiz: Write a Proof that shows that ∆ABC = ∆FDE.Given: <C = <E, <D = <B, and CA = EF
A
BC
DE
F
CPCTCIf two triangles are congruent, then each part of one triangle is
congruent to the corresponding part of the other triangle.
CPCTCFind the length of DC.Given: BA = ED
<B = <E AB = 12 in BC = 13 in AC = 15 in
B
A
C
D
E
CPCTCFind the length of the missing sides/angles.
A
BC
D
E
F
AB
C
D
E46˚
35˚
58˚
62˚
Given: ∆ABC = ∆EFD Given: ∆ABC = ∆DBE
5 cm
7 cm
4 cm
9 cm
8 cm
CPCTC
338 Chapter 6 | Congruence
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1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
Proof
338 Chapter 6 | Congruence
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1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
CPCTC: Group 1
338 Chapter 6 | Congruence
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Car
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1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
Proof
338 Chapter 6 | Congruence
© 2
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Car
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ng, I
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6
1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
CPCTC: Group 2
Lesson 6.4 | CPCTC 339
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6CPCTC makes it possible to prove other theorems. For example:
The Isosceles Triangle Base Angle Theorem states: “If two sides of a triangle are congruent, then the angles opposite these sides are congruent.”
To prove the Isosceles Triangle Base Angle Theorem, you need to add an auxiliary line to an isosceles triangle that bisects the vertex angle as shown.
1. Create a two-column proof. Given:
___ GB !
____ GD
Prove: !B ! !D D
UG
B
Statements Reasons
PROBLEM 2 Isosceles Triangle Base Angle Theorem and Its Converse
Proof
338 Chapter 6 | Congruence
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1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
CPCTC: Group 3
340 Chapter 6 | Congruence
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The Isosceles Triangle Base Angle Converse Theorem states: “If two angles of a triangle are congruent, then the sides opposite these angles are congruent.”
To prove the Isosceles Triangle Base Angle Converse Theorem, you need to add an auxiliary line to an isosceles triangle that bisects the vertex angle as shown.
2. Create a two-column proof. D
UG
B
Given: !B ! !D Prove:
___ GB !
____ GD
Statements Reasons
1. How wide is the horse’s pasture?
PROBLEM 3 Applications
Proof
338 Chapter 6 | Congruence
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1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
CPCTC: Group 4
532 Chapter 6 ! Skills Practice
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Problem Set
Create a two-column proof to prove each statement.
1. Given: ___
RS is the ! bisector of ___
PQ .
R
Q
S
P
T Prove: !SPT ! !SQT
Statements Reasons
1. ___
RS is the ! bisector of ___
PQ . 1. Given
2. ___
RS ! ___
PQ 2. Definition of perpendicular bisector
3. "PTS and "QTS are right angles. 3. Definition of perpendicular lines
4. #PTS and #QTS are right triangles. 4. Definition of right triangles
5. ___
RS bisects ___
PQ. 5. Definition of perpendicular bisector
6. ___
PT ! ___
QT 6. Definition of bisect
7. ___
TS ! ___
TS 7. Reflexive Property of !8. #PTS ! #QTS 8. Leg-Leg Congruence Theorem
9. "SPT ! "SQT 9. CPCTC
2. Given: ___
TZ ! ____
WX , ___
TM ! ____
WT , and ___
TZ " ____
WX M
T
WX
Z
Prove: ____
MZ ! ___
TX
Proof
338 Chapter 6 | Congruence
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6
1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
CPCTC: Group 5
Chapter 6 ! Skills Practice 533
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Name _____________________________________________ Date ____________________
6
3. Given: ___
AG and ___
EK intersect at C, A
CE
G
K
___
AC ! ___
EC , ___
CK ! ____
CG
Prove: !K ! !G
4. Given: !JHK ! !LHK, !JKH ! !LKH
JL
H
K
Prove: ___
JK ! ___
LK
Proof
338 Chapter 6 | Congruence
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6
1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U
Home Work
Chapter 6 ! Assignments 115
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Assignment Assignment for Lesson 6.4
Name _____________________________________________ Date ____________________
CPCTC Corresponding Parts of Congruent Triangles are Congruent
1. What is the width of the swimming pool? Explain how you got your answer.
84 ft
82 ft
82 ft
2. Marcel is painting the triangular section of a shuffleboard court shown in the figure. He starts by putting 41 feet of tape around the outside of the triangle. He knows that the base of the triangle is 16 feet and each base angle of the triangle measures 50 degrees. What is the length of each leg?
50° 50°
16 ft
340 Chapter 6 | Congruence
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The Isosceles Triangle Base Angle Converse Theorem states: “If two angles of a triangle are congruent, then the sides opposite these angles are congruent.”
To prove the Isosceles Triangle Base Angle Converse Theorem, you need to add an auxiliary line to an isosceles triangle that bisects the vertex angle as shown.
2. Create a two-column proof. D
UG
B
Given: !B ! !D Prove:
___ GB !
____ GD
Statements Reasons
1. How wide is the horse’s pasture?
PROBLEM 3 Applications
Home Work
Lesson 6.4 | CPCTC 341
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2. Calculate AP if the perimeter of !AYP is 43 cm.
P
Y
A 13 cm
70°
70°
3. Lighting booms on a Ferris wheel consist of four steel beams that have cabling with light bulbs attached. These beams along with 3 shorter beams form the edges of three congruent isosceles triangles as shown. Maintenance crews are installing new lighting along the four beams. Calculate the total length of lighting needed.
4. Calculate m"T.
W M
117°
T
Lesson 6.4 | CPCTC 341
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2. Calculate AP if the perimeter of !AYP is 43 cm.
P
Y
A 13 cm
70°
70°
3. Lighting booms on a Ferris wheel consist of four steel beams that have cabling with light bulbs attached. These beams along with 3 shorter beams form the edges of three congruent isosceles triangles as shown. Maintenance crews are installing new lighting along the four beams. Calculate the total length of lighting needed.
4. Calculate m"T.
W M
117°
T
Home Work
342 Chapter 6 | Congruence
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5. What is the width of the river?
6. Given: ___
ST ! ___
SR , ___
TA ! ___
RA Explain why !T ! !R.
S
R
A
T
Be prepared to share your solutions and methods.
Proof
338 Chapter 6 | Congruence
© 2
010
Car
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ng, I
nc.
6
1. Create a two-column proof.
Given: ____
CW and ___
SD bisect each other Prove:
___ CS !
____ WD
Statements Reasons
2. Create a two-column proof.
Given: ___
SU " ___
SK , ___
SR " ___
SH Prove: !U " !K
Statements Reasons
C
S
P D
W
S H K
R
U