Name Period 11/2 11/13

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Name _________________________________________ Period ____ 11/2 – 11/13

G

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M

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T

R

Y

U

N

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6

6 –

–

C

O

N

G

R

U

E

N

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R

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A

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Vocabulary Terms:

Congruent Corresponding Parts Congruency statement Included angle Included side HL Non-included side Hypotenuse Leg SSS SAS ASA AAS Friday, 11/2

Chapter 4 Section 3: Congruent Triangles

I can match the corresponding parts of congruent figures given a picture or a congruency statement. I can prove polygons congruent using the definition of congruent polygons.

ASSIGNMENT: Pg. 234 (#2-11, 13-16, 19, 21-22, 28-31) Completed: Monday, 11/5

Chapter 4 Section 4: Triangle Congruence: SSS and SAS

I can determine if 2 triangles are congruent using SSS or SAS.

ASSIGNMENT: Triangle Congruence WST - #2, 4, 8, 9, 13, 15, 16, 19 Completed:

Tuesday, 11/6

Chapter 4 Section 5: Triangle Congruence: ASA, AAS, and HL

I can determine if 2 triangles are congruent using ASA, AAS, or HL.

ASSIGNMENT: Triangle Congruence WST - Finish Completed:

Wednesday or Thursday, 11/7-8

Chapter 4 Section 4 and 5: Triangle Congruence: SSS and SAS AND ASA, AAS, and HL

I can determine if 2 triangles are congruent using SSS, SAS, ASA, AAS, or HL.

I can determine the missing piece of information needed to prove triangles congruent I can complete a fill-in-the-blank proof.

I can use triangle congruence and logic to solve problems.

ASSIGNMENT: Triangle Congruence and Logic Worksheet Completed:

Friday, 11/9

Chapter 4 Section 6: CPCTC

I can use CPCTC to solve different types of problems. I can use CPCTC in geometric proofs

ASSIGNMENT: CPCTC Worksheet Completed:

11/2 Congruent Polygons 11/5 SSS and SAS 11/6 ASA, AAS, HL 11/7-8 Congruent Triangles and Logic 11/9 CPCTC 11/12 Review 11/13

Test

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Monday, 11/12

Tuesday, 11/13

If you miss the review day, you are still expected to take the test on the test day.

For more help BEFORE the test:

1. Use the indicated chapters in your book

2. Use the book online (it has videos and a homework help section)

3. Use Google to find more resources

4. Come to tutoring (with assignment)

Review Day

ASSIGNMENT: Review for Test

Completed:

Test Day

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CONGRUENT Polygons Examples

I. Name the congruent triangles.

1.

LIN ≅

_______ 2.

FOX ≅

______

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

3. FGH ≅______ _____ EFI ≅ FG ≅ _____ _____ G ≅ GH ≅ _____ _____ H ≅ FH ≅ _____

Use the congruency statement to fill in the corresponding congruent parts. 4. EFI ≅HGI _{E ≅}_{_____} FE ≅_____ _____ EFI ≅ FI ≅ _____ _____ FIE ≅ IE ≅ _____ B O X F O X L I N E A R

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Example 3: Proving Triangles Congruent Given: ∠YWX and ∠YWZ are right angles.

YW_{bisects ∠XYZ. W is the midpoint of XZ. XY ≅ YZ.}

Prove: ∆XYW ≅ ∆ZYW

Check It Out! Example 3 Given: AD bisects BE. BE_{bisects AD.}

AB_{≅ DE, ∠A ≅ ∠D}

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Check It Out! Example 4

Use the diagram to prove the following.

Given: MK bisects JL. JL bisects MK. JK ≅ ML. JK || ML. Prove: ∆JKN ≅ ∆LMN

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Name ________________________________________________ Period ______________ Triangle Congruence

1. List the five ways to prove that triangles are congruent.

______________ ______________ ______________ ______________ ______________

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

2. ∆ABC ≅ ∆EFD ______________ 3. ∆AEC ≅ ∆BED ______________

4. ∆ABC ≅ ∆EFD ______________ 5. ∆ADC ≅ ∆BDC ______________

6. ∆ACE ≅ ∆DBE ______________ 7. ∆ADC ≅ ∆BDC ______________

8. ∆ABC ≅ ∆CDA ______________ 9. ∆ABE ≅ ∆CDE ______________

10. ∆CAE ≅ ∆DBE ______________ 11. ∆MAD ≅ ∆MBC ______________

C A B D F E C D A E B A C B D F E A D B C A C E D B A C B D C A D B C A E D B _D A C B M A B E C D

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12. ∆DCA ≅ ∆DCB ______________ 13. ∆ACB ≅ ∆ADB ______________

14. ∆RTQ ≅ ∆STP ______________ 15. ∆DBA ≅ ∆BDC ______________

16. ∆AEB ≅ ∆DEC ______________ 17. ∆CDE ≅ ∆ABF ______________

18. ∆DEA ≅ ∆BEC ______________ 19. ∆HIJ ≅ ∆QOP ______________

20. ∆RTS ≅ ∆CAB ______________ 21. ∆ABC ≅ ∆ADC ______________

7. ∆BAP ≅ ∆BCP ______________ 8. ∆SAT ≅ ∆SAR ______________

A D B C T P S R Q A C D B C B D A A E C D B A D E F B C A B C D E _H J I P Q O T _S R B C A A B D C B A P C D T S R A

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Name ______________________________________________ Period _______________ Triangle Congruence and Logic Worksheet

I. 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. a. ______________ a. ______________ a. ______________ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ c. ______________ c. ______________ c. ______________ 4. 5. 6. a. ______________ a. ______________ a. ______________ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ c. ______________ c. ______________ c. ______________ 7. 8. 9. a. ______________ a. ______________ a. ______________ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ b. ∆_____ ≅ ∆ _____ c. ______________ c. ______________ c. ______________ A _B D E C A B C D A B C E _D M L S I E I W H S _L O V E A W T E R L _U G E H T A M P

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

10. SAS 11. ASA 12. SSS

_______ ≅ ________ ________ ≅ ________ _______ ≅ _______

13. AAS 14. HL 15. ASA

_______ ≅ ________ ________ ≅ ________ _______ ≅ _______

III. Multiple Choice

16. Which set of coordinates represents the vertices of a triangle congruent to ∆RST? (Hint: Find the lengths of the sides of ∆RST)

A. (3, 4) (3, 0) (0, 0) B. (3, 3) (0, 4) (0, 0) C. (3, 1) (3, 3) (4, 6) D. (3, 0) (4, 4) (0, 6)

17. Given ∆ABC and ∆DEF. Which of the following pairs of corresponding parts would correctly prove the triangles congruent by ASA?

A. ∠B≅ ∠E,∠A≅ ∠D AB, ≅DE _B.∠_C≅ ∠_F_,∠_A≅ ∠_{D AB}_, ≅_DE C. ∠B≅ ∠E,∠C≅ ∠F AB, ≅DE _D.∠_B≅ ∠_E_,∠_A≅ ∠_{D AC}_, ≅_DF F A D E B C C A B D E F A B C D P S T R Q P R S Q D _C B A R S T 2 4 6 2 4 6 x y

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For 18 – 19: Fill in the blank with the correct statement or reason to complete the proofs.

18. GIVEN: RZ bisects TS; ∠3 ≅ ∠4 PROVE: ∆RZS ≅ ∆RZT

A. Reflexive Property B. Given C. ∠3 ≅ ∠4

D. E. SAS

19. GIVEN: ∠Q ≅ ∠S;

R is the midpoint of QS . PROVE: ∆PRQ ≅ ∆TRS

A. ∠PRQ ≅ ∠SRT B. Definition of midpoint C. ASA

D. Given E. R is the midpoint of QS

20. 21. Given: E is the midpoint of AB,C≅D

Which of the following statements must be true? A A≅D B AE≅ED C _CE≅_ED D CD≅BA STATEMENTS REASONS 1. RZ bisects TS

2. Definition of a segment bisector

3. Given 4. RZ ≅RZ 5. ∆RZS ≅ ∆RZT R S T Z 4 3 1 2

R

S T P

Q

STATEMENTS REASONS 1. ∠Q ≅ ∠S 2. Given 3. QR≅RS

4. Vertical Angle Theorem

5. ∆PRQ ≅ ∆TRS

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22. In the figure below, AC≅DFand C≅F Which additional information would be

enough to prove ∆ABC

≅

∆DEF?

AAB≅DE B AB≅BC C BC≅EF D BC≅DE 23. 24.

24. Draw a counterexample for the following statement.

If the 3 angles in one triangle are congruent to the corresponding angles in another triangle, then the 2 triangles are congruent.

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I. CPCTC stands for ___________________________________________________________________________. This means that once you have proven the 2 triangles _______________________, you know that all the

_________________________ parts are also ____________________.

Examples: 1) Find JK

2)

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Q R N M P 35o x° A 21° (3y)° 7 y 3y + 20 B C A D CPCTC Worksheet

I. Solve for the variable.

1. CAT ≅DOG_{. Find h.} _{2. IEF} ≅_HGF_{. Find a.}

3. PQR ≅MNR_{. Find x.} _4._ABC≅_ADC_._{Find y.}

II. Set up an equation and then solve for the variable.

5. CAT ≅DOG_{. Find x.} _{6. IEF} ≅_HGF_{. Find a.}

7. ABD≅CDB._{Find x.} _8._ABD≅_CDB_._{Find y.}

A T C O G DD h 15 A T C O G DD (3x+9) (8x-6) (2a+3) o (5a) o F G H I E a° 38° B C D F G H I E B C A D (4x-35)o (2x+17)o

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III. For which value(s) of x are the triangles congruent? 9. x = _______________ 10. x = _______________ 11. x = _______________ 12. x = _______________ 13. x = _______________ 14. x = _______________ 15. x = _______________ 16. x = _______________ D _B E A C 92° 5x° A D 1 m ∠3 = 3x m ∠4 = 7x - 10 B E C 2 3 4 4x + 8 7x - 4 A B R C m ∠ CDB = (15x + 3)° m ∠ ABD = (10x + 18)° 19 D A B C 9x - 8 D C A B D C (2x + 4)° 1 2 B A (4x – 6)° W S R Z T x2_{+ 2x} x2_{+ 24} 5x - 8 F D E 3x + 2 C A B

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IV. Proofs

17. GIVEN: N is the midpoint of AB AX ≅NY NX ≅BY PROVE: ∠X ≅ ∠Y 18. GIVEN: RT ≅RV TS ≅VS PROVE: ∠RST ≅ ∠RSV 19. GIVEN: VB bisects ∠EVO BV bisects ∠EBO PROVE: ∠E ≅ ∠O

STATEMENTS

REASONS 1. N is the midpoint of AB 2. Definition of a midpoint 3. AX ≅NY 4. Given 5. AXN ≅NYB 6. CPCTC

STATEMENTS

REASONS 1. Given 2. 3. Reflexive 4. SSS 5. ∠RST ≅ ∠RSV R T S V A X N Y B STATEMENTS REASONS 1. VB bisects ∠EVO

2. Definition of Angle Bisector

3. Given 4. ∠ ≅ ∠1 2 5. BV ≅BV 6. ASA 7. ∠E ≅ ∠O B V O E 1 2 3 4