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Transcript 
Geometry Section 4-2D
Corresponding Parts
Pg. 274
Be ready to grade 4-2C
Quiz Tuesday!!!
Exam Review Questions Monday.
1
Answers for 4-2C
1.
2.
3.
4.
5.
6.
7.
8.
9.
Complimentary
True
True
C – 50.2o, S – 140.2o
C – 41o,
S – 131o
C – 53 ½o , S – 143 ½o
C – 23o,
S – 113o
mDBC = 52 ½o, mDBE = 127 ½o
mABD = 47o, mDBC = 43 o
2
Answers for 3-3C – cont.
mEBD = 136o, mABD = 46o
11. mDBC = 52o,
mABD = 38o
12. mDBC = 52o,
mABD = 38o
13. 57o
10.
Book:
16. No, if the window ledge is straight, both
angles will = 90o.
17. 35o
3
Explore
Given: AE @ CE
ABE @ CDE
AEB and CED are rt. ’s
B
C
Prove: AB @ CD
A
Statements:
E
D
Reasons
b. AE @ CE
Given
d. ABE @ CDE
Given
c. AEB and CED are rt. angles
a. AEB @ CED
Given
f. rAEB @ rCED
SAA
e. AB @ CD
Def. of @ triangles
Right angles are @
4
Theorem:
Corresponding parts of congruent triangles
are congruent.
CPCTC
If you can prove that triangles are congruent using a
previous postulate, then you can prove that all parts of
the triangles are congruent by using CPCTC.
5
Example:
X
W
Given: XY @ ZW
YZ @ WX
Prove: WX || YZ
Y
Z
6
Properties of Congruence:
Properties of Congruence
Examples
Reflexive
Symmetric
Transitive
AB @ AB
If 1 @ 2 then 2 @ 1
If WX @ XY and XY @ YZ then WX @ YZ
B
A
AB @ AB
7
V
Try It:
S
T
U
How can you prove that the triangles are congruent by
using the SAS Postulate?
a. 1 marked angle and 1 marked side + the
reflexive property.
Which additional pairs of sides and angles could you
then prove congruent by using CPCTC?
b. SV @ VU, VST @ VUT and SVT @ UVT
8
Exercises
C
A
T
B
R
S
1. Write a triangle congruence statement for the triangles shown.
rABC @ rRST
b. Which congruence postulate can be used to prove the
triangles are congruent? SSS
c. Once you prove the triangles are congruent, how can
you show that C @ T? CPCTC
9
B
#4
A
C
Given: AC bisects BAD, and CA bisects BCD
D
Prove: AD @ AB
10
G
H
F
E
Statements
Reasons
Given
Given
Reflexive
SSS
CPCTC
a. rGFH @ rEFH
b. EF @ GF
c. HF @ HF
d. GFH @ EFH
e. EH @ GH
11
R
S
U
Statements:
Reasons
RU @ ST
Given
US @ US
Reflexive Property
RUS @ TSU
Given
rRSU @ rTUS
SUT @ USR
SAS
RS || UT
T
CPCTC
Alt. Int. ‘s Theorem
12
D
C
3
1
4
2
A
a. 2
e. DCBA
b. 1
f. ASA
c. Alt. Int. ‘s are @
g. CPCTC
B
d. Reflexive
13
Homework: Practice 4-2D
14
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