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Geometry Section 4-2DGeometry Section 4-2D

Corresponding PartsCorresponding Parts

Pg. 274Pg. 274

Be ready to grade 4-2CBe ready to grade 4-2CQuiz Tuesday!!!Quiz Tuesday!!!

Exam Review Questions Exam Review Questions Monday.Monday.

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Answers for 4-2CAnswers for 4-2C

1. Complimentary2. True3. True4. C – 50.2o, S – 140.2o

5. C – 41o, S – 131o

6. C – 53 ½o , S – 143 ½o

7. C – 23o, S – 113o

8. mDBC = 52 ½o, mDBE = 127 ½o

9. mABD = 47o, mDBC = 43 o

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Answers for 3-3C – cont.Answers for 3-3C – cont.10.mEBD = 136o, mABD = 46o

11.mDBC = 52o, mABD = 38o

12.mDBC = 52o, mABD = 38o

13.57o

Book:16.No, if the window ledge is

straight, both angles will = 90o.17.35o

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ExploreExplore

Statements: Reasons

c. AEB and CED are rt. angles

Given

Right angles are

b. AE CE

Givend. ABE CDE

Given

a. AEB CED

f. AEB CED SAA

e. AB CD Def. of triangles

E

C

A

B

D

Given: AE CEABE CDEAEB and CED are rt. ’s

Prove: AB CD

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Theorem: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.

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Example:Example:Given: XY ZW

YZ WX

Prove: WX || YZZ

W

Y

X

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Properties of Congruence: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

A

B

AB AB

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Try It:Try It:

a.

b.

1 marked angle and 1 marked side + the reflexive property.

SV VU, VST VUT and SVT UVT

T

V

S U

How can you prove that the triangles are congruent by using the SAS Postulate?

Which additional pairs of sides and angles could you then prove congruent by using CPCTC?

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ExercisesExercises

R S

T

A B

C

1. Write a triangle congruence statement for the triangles shown.ABC RST

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

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#4#4

D

B

A C

Given: AC bisects BAD, and CA bisects BCD

Prove: AD AB

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Statements Reasons

a. GFH EFH d. GFH EFH

e. EH GHb. EF GFc. HF HF

Given

Given

Reflexive

SSS

CPCTC

E

G

FH

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R

U

S

T

Statements: Reasons

RUS TSU

Given

Given

RU ST

Reflexive Property US US

SAS

SUT USR

RSU TUS

CPCTC

RS || UT Alt. Int. ‘s Theorem

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D

A

C

B

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3 4

a. 2

b. 1

c. Alt. Int. ‘s are

d. Reflexive

e. CBA

f. ASA

g. CPCTC

14Homework: Practice 4-2D