Geometry NAME Worksheet – Congruent Triangles Date HR a ...

[Pages:13]Geometry Worksheet ? Congruent Triangles

NAME _____________________ Date ______________HR ______

a) Determine whether the following triangles are congruent. b) If they are, name the triangle congruence (pay attention to proper correspondence when naming the triangles) and then identify the Theorem or Postulate (SSS, SAS, ASA, AAS, HL) that supports your conclusion. c) Be sure to show any additional congruence markings you used in your reasoning. d) If the triangles cannot be proven congruent, state "not possible." Then given the reason it is not possible.

1)

2)

3)

Congruence:

ABD _________

Congruence:

EFG _________

Congruence:

EMN _________

Reason:

Reason:

Reason:

4)

5)

6)

Congruence:

STU ________

Reason:

Congruence:

YZA ________

Reason:

Congruence:

CDE ________

Reason:

7)

8)

9)

Congruence:

KJM ________

Reason:

Congruence:

NPR ________

Reason:

Congruence:

STU ________

Reason:

10)

11)

12)

|

Congruence:

XYZ ________

Reason:

Congruence:

DEG ________

Reason:

Congruence:

HJK ________

Reason:

13)

14)

15)

Congruence:

STV ________

Reason:

Congruence:

WXY ________

Reason:

Congruence:

BCF ________

Reason:

16)

17)

18)

Congruence:

GJK ________

Reason:

Congruence:

KLP ________

Reason:

Congruence:

NSQ ________

Reason:

19)

20)

21)

Congruence:

LMN ________

Reason:

Congruence:

STV ________

Reason:

Congruence:

WXY ________

Reason:

22)

23)

24)

S

Congruence:

BCE ________

Reason:

Congruence:

GHJ ________

Reason:

Congruence:

NPM ________

Reason:

25)

26)

27)

Congruence:

TUV ________

Reason:

Congruence:

BCZ ________

Reason:

Congruence:

EFG ________

Reason:

Use the given information to mark the diagram appropriately. Name the triangle congruence (pay attention to proper correspondence when naming the triangles) and then identify the Theorem or Postulate (SSS, SAS, ASA, AAS, HL) that would be used to prove the triangles congruent. If the triangles cannot be proven congruent, state "not possible."

28)

29)

Given: CD AB; B D

Congruence:

CDE ________

Reason:

30)

Given: JN LM ; NK MK; N M

Congruence:

JKN ________

Reason:

31)

Given: AC BD; AD BC

Congruence:

ABC ________

Reason:

Given: SQ and PR bisect each other

Congruence:

RST ________

Reason:

32)

Given: GH bisects EGF ;

EG FG

Congruence: EGH ________

Reason:

Now choose one of the problems from 28-32 and create a flow chart proof. Then transform your flow chart proof into a 2 column proof. Your "given" will be the "Given" from the problem and your "prove" will be the "Congruence" statement you created.

Worksheet # 79

Using CPCTC with Triangle Congruence

Name ________________________________ Period ______

1. Fill in the missing statements and reasons.

A

B

Given: AB || DC , B D Prove: BC DA

D

C

Statements

1. ______________________________ 2. BAC DCA

3. ______________________________

4.

AC AC

5. ABC CDA

6. ______________________________

2. Complete the two-column proof.

Reasons

1. Given

2. ________________________________________

3. Given

4. ________________________________________

5. ___________ Congruence Theorem

6. CPCTC

Q K

Given: QK QA, QB bisects KQA

A

Prove: KB AB

Statements 1. ______________________________ 2. QB bisects KQA 3. ______________________________ 4. ______________________________ 5. KBQ __________ 6. ______________________________

Reasons

B

1. Given

2. ________________________________________

3. Definition of Bisector

4. Reflexive Property of Congruence

5. ___________ Congruence Postulate

6. ________________________________________

3. Fill in the missing statements and reasons.

A

B

Given: BD AB, BD DE, AB DE

C

Prove: A E

Statements

Reasons

D

E

1. ______________________________ 2. B & D are right angles

1. ________________________________________ 2. Definition of _____________________________

3. ______________________________

4. BCA ECD

5.

AB DE

6. ABC __________

3. All ____________ angles are congruent 4. ________________________________________ 5. ________________________________________ 6. ___________ Congruence __________________

7. _____________________________

7. ________________________________________

4. Complete the two-column proof.

Given: FJ GH, JFH GHF Prove: FG JH

Statements

1. __________________________

2.

JFH GHF

3.

FH HF

4. __________ __________

5. __________________________

F

G

J

H

Reasons

1. ________________________________________

2. Given

3. ________________________________________

4. ___________ Congruence __________________

5. ________________________________________

5. Fill in the missing statements and reasons.

Given: MN MP, MP PO, MN NO Prove: NOM POM

Statements 1. MP PO, MN NO 2. ___________________________________________ 3. ___________________________________________ 4. ___________________________________________ 5. ___________________________________________ 6. __________ __________ 7. ___________________________________________

M

P

N

C

O

Reasons 1. ________________________________________ 2. Definition of Perpendicular 3. Definition of Right Triangle 4. Given 5. ________________________________________ 6. ___________ Congruence __________________ 7. ________________________________________

6. Complete the two-column proof.

Given: CN AB, CN bisects ACB Prove: ABC is an isosceles triangle

Statements 1. _____________________________________ 2. ANC & BNC are right angles 3. _____________________________________ 4. _____________________________________ 5. _____________________________________ 6. _____________________________________ 7. ANC __________ 8. AC ________ 9. _____________________________________

C

A

N

B

Reasons

1. ________________________________________

2. Definition of _____________________________

3. All right angles are ________________________

4. Given

5. Definition of _____________________________

6. ________________________________________

7. _______________ Congruence Postulate

8. ________________________________________

9. Definition of _____________________ Triangle

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