Triangle Congruence 2 - Dunkerton High School



Unit #7: Triangle Congruence

Congruent Polygons

SSS

SAS

AAS

HL

ASA

Congruence Statement

Corresponding Parts

CPCTC

Dates, assignments, and quizzes subject to change without advance notice

|Monday |Tuesday |Block Day |Friday |

| | |7/8 |9 |

| | |Congruent Polygons |ASA, AAS, and HL |

| | |SSS and SAS | |

|12 |13 |14/15 |16 |

|Proofs |QUIZ |Review |TEST |

| |CPCTC |TEST – (Proofs) | |

Wednesday, 11/7/12 or Thursday, 11/8/12

|4-3 and 4-4: Congruent Triangles, SSS and SAS |

• I can use the properties of equilateral triangles to find missing side lengths and angles.

• I can write a congruency statement representing two congruent polygons.

• I can identify congruent parts of a polygon, given a congruency statement.

• I can prove triangles are congruent using SSS, ASA.

PRACTICE: pg. 234 #3-11, 19, 22-25, 31 (15 problems) Triangle Congruence Worksheet #1

Friday, 11/9/12

|4-5: ASA, AAS, and HL |

• I can prove triangles are congruent using ASA, AAS, and HL

• I can mark pieces of a triangle congruent given how they are to be proved congruent.

PRACTICE: Triangle Congruence Worksheet #2

Monday, 11/12/12

|Triangle Congruence Proofs |

• I can write a two-column proof to show that two triangles are congruent.

PRACTICE: Triangle Proofs Worksheet Part 1

Tuesday, 11/13/12

|4-6: Triangle Proofs with CPCTC ( QUIZ |

• I can write a two-column proof to show that two triangles are congruent.

PRACTICE: Triangle Proofs Worksheet Part 2

Wednesday, 11/14/12 or Thursday, 11/15/12

|Review ( Test: Triangle Properties (Proofs) |

• I can assess my knowledge and prepare for the test.

PRACTICE: Review Worksheet

Friday, 11/16/12

|( Test: Triangle Properties |

I. Name the congruent triangles.

1.[pic] 2. [pic]

3. [pic] 4. [pic]

II. Name the congruent triangle and the congruent parts..

7. [pic]

[pic] [pic][pic]

[pic] [pic][pic]

[pic] [pic][pic]

Use the congruency statement to fill in the corresponding congruent parts.

8. [pic] [pic] [pic][pic] [pic]

[pic][pic] [pic] [pic][pic]

9. [pic]. Find x. 10. [pic] Find y.

Third Angles Theorem (add to Theorems, Postulates and Definitions Card) –

Triangle Congruence Worksheet #1

For each pair of triangles, tell which postulates, if any, make the triangles congruent.

12. (ABC ( (EFD ______________ 13. (ABC ( (CDA ______________

14. (ABC ( (EFD ______________ 15. (ADC ( (BDC ______________

21. (MAD ( (MBC ______________ (ABE ( (CDE ______________

23. (ACB ( (ADB ______________ 23. ______________

23. ______________

Triangle Congruence Worksheet #2

I. For each pair of triangles, tell which postulate, if any, can be used to prove the triangles congruent.

1. (AEB ( (DEC ______________ 2. (CDE ( (ABF ______________

3. (DEA ( (BEC ______________ 4. (AGE ( (CDF ______________

5. (RTS ( (CBA ______________ 6. (ABC ( (ADC ______________

7. (BAP ( (BCP ______________ 8. (SAT ( (SAR ______________

Given: BD bisects ABC

II. For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give the postulate that makes them congruent.

1. 2. 3. Given: T is the midpoint of WR

a. ______________ a. ______________ a. ______________

b. (_____ ( ( _____ b. (_____ ( ( _____ b. (_____ ( ( _____

c. ______________ c. ______________ c. ______________

4. 5. Given: IH Bisects WIS 6.

[pic]

a. ______________ a. ______________ a. ______________

b. (_____ ( ( _____ b. (_____ ( ( _____ b. (_____ ( ( _____

c. ______________ c. ______________ c. ______________

7. 8. 9.

a. ______________ a. ______________ a. ______________

b. (_____ ( ( _____ b. (_____ ( ( _____ b. (_____ ( ( _____

c. ______________ c. ______________ c. ______________

10. Given: I is the midpoint 11. 12.

of ME and SL

a. ______________ a. ______________ a. ______________

b. (_____ ( ( _____ b. (_____ ( ( _____ b. (_____ ( ( _____

c. ______________ c. ______________ c. ______________

III. Using the given postulate, tell which parts of the pair of triangles should be shown congruent.

1. SAS 2. ASA 3. SSS

_______ ( ________ ________ ( ________ _______ ( _______

4. AAS 5. HL 6. ASA

_______ ( ________ ________ ( ________ _______ ( _______

For each problem below, write a two-column proof on a separate piece of paper.

I. Proving Triangles Congruent:

1. 5.

2.

3. 6.

4.

II. Using CPCTC

7. 10.

8. 11.

9.

Review: Triangles and Triangle Congruence

You will need a separate piece of paper to show all your work. This review is not comprehensive; always be sure to go back through your old homework and quizzes.

← I can write a congruency statement representing two congruent polygons

1. Write a congruency statement for the two triangles at right.

← I can identify congruent parts of a polygon, given a congruency statement

2. List ALL of the congruent parts if [pic]

← I can use algebra to find the side lengths and angle measures of congruent polygons

3. [pic] Find p.

4. [pic] Find x.

← I can name the five ways to prove triangles are congruent

5. Name the 5 ways to prove triangles congruent.

← I can prove triangles are congruent

For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give the postulate that makes them congruent.

6.

7.

8. Given: I is the midpoint

of ME and SL

← I can mark pieces of a triangle congruent given how they are to be proved congruent

7. What information is

9. missing to use HL?

10. What information is missing to use SAS?

IV. For which value(s) of x are the triangles congruent?

3. x = _______________ 4. x = _______________

5. x = _______________

← I can write a two-column proof over congruent triangles

11.

[pic]

12. Complete and review ALL proofs on the proofs worksheet.

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C

O

G

R

A

E

A

I

B

O

X

F

O

X

E

L

R

N

R

Q

N

M

P

x°

A

B

C

D

(3y)°

21°

35o

C

A

D

B

C

A

B

D

F

E

A

B

D

C

A

C

B

D

F

E

A

B

E

C

D

D

A

C

B

M

A

C

D

B

A

E

C

D

B

A

D

E

F

B

C

A

B

C

D

E

A

B

D

C

T

S

R

B

C

A

A

T

S

R

A

D

B

P

C

L

O

V

E

E

A

A

B

D

E

C

T

R

W

L

U

G

E

S

H

W

I

H

P

A

T

M

C

F

L

M

I

E

S

D

A

B

E

A

B

C

D

C

A

B

D

E

F

F

A

D

E

B

C

P

R

S

Q

D

C

B

A

P

S

T

R

Q

1

2

C

A

R

G

E

O

X

Y

W

Z

V

2

2p

20

(7p+13)

D

C

(2x[pic] + 7)°

1

2

B

A

(x[pic] – 8x)°

A

B

C

D

A

W

T

E

R

S

L

M

I

E

P

R

S

Q

D

C

A

B

A

D

1

m (3 = x2

m (4 = 7x - 10

B

E

C

2

3

4

4x + 8

7x - 4

A

B

R

C

W

S

R

Z

T

x2 + 2x

x2 + 24

x2 + 3x

D

A

B

C

9x - 8

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