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Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation...

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Holt McDougal Geometry Triangle Congruence: CPCTC Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Lesson Presentation Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry
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Page 1: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTCTriangle Congruence: CPCTC

Holt Geometry

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt McDougal Geometry

Page 2: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Warm-up

Identify the postulate or theorem that proves the triangles congruent.

ASAHL

SAS or SSS

Page 3: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Warm-up

4. Given: PN bisects MO, PN MO

Prove: ∆MNP ∆ONP

1. Given2. Def. of bisect3. Reflex. Prop. of 4. Given5. Def. of 6. Rt. Thm.7. SAS

1. PN bisects MO2. MN ON3. PN PN4. PN MO 5. PNM and PNO are rt. s6. PNM PNO

7. ∆MNP ∆ONP

Reasons Statements

Page 4: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Use CPCTC to prove parts of triangles are congruent.

Objective

Page 5: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent.

Page 6: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent.

Remember!

Page 7: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Example 2: Proving Corresponding Parts Congruent

Prove: XYW ZYW

Given: YW bisects XZ, XY YZ.

Z

Page 8: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Example 2 Continued

WY

ZW

Page 9: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Check It Out! Example 2

Prove: PQ PS

Given: PR bisects QPS and QRS.

Page 10: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Check It Out! Example 2 Continued

PR bisects QPS

and QRS

QRP SRP

QPR SPR

Given Def. of bisector

RP PR

Reflex. Prop. of

∆PQR ∆PSR

PQ PS

ASA

CPCTC

Page 11: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Work backward when planning a proof. To show that ED || GF, look for a pair of angles that are congruent.

Then look for triangles that contain these angles.

Helpful Hint

Page 12: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Example 3: Using CPCTC in a Proof

Prove: MN || OP

Given: NO || MP, N P

Page 13: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

5. CPCTC5. NMO POM

6. Conv. Of Alt. Int. s Thm.

4. AAS4. ∆MNO ∆OPM

3. Reflex. Prop. of

2. Alt. Int. s Thm.2. NOM PMO

1. Given

ReasonsStatements

3. MO MO

6. MN || OP

1. N P; NO || MP

Example 3 Continued

Page 14: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Check It Out! Example 3

Prove: KL || MN

Given: J is the midpoint of KM and NL.

Page 15: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Check It Out! Example 3 Continued

5. CPCTC5. LKJ NMJ

6. Conv. Of Alt. Int. s Thm.

4. SAS4. ∆KJL ∆MJN

3. Vert. s Thm.3. KJL MJN

2. Def. of mdpt.

1. Given

ReasonsStatements

6. KL || MN

1. J is the midpoint of KM and NL.

2. KJ MJ, NJ LJ

Page 16: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Lesson Quiz: Part I

1. Given: Isosceles ∆PQR, base QR, PA PB

Prove: AR BQ

Page 17: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

4. Reflex. Prop. of 4. P P

5. SAS5. ∆QPB ∆RPA

6. CPCTC6. AR = BQ

3. Given3. PA = PB

2. Def. of Isosc. ∆2. PQ = PR

1. Isosc. ∆PQR, base QR

Statements

1. Given

Reasons

Lesson Quiz: Part I Continued

Page 18: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Lesson Quiz: Part II

2. Given: X is the midpoint of AC . 1 2

Prove: X is the midpoint of BD.

Page 19: Holt McDougal Geometry Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Holt McDougal Geometry

Triangle Congruence: CPCTC

Lesson Quiz: Part II Continued

5. CPCTC

4. ASA4. ∆AXD ∆CXB

6. Def. of mdpt.6. X is mdpt. of BD.

3. Vert. s Thm.3. AXD CXB

2. Def. of midpt.2. AX CX

1. Given1. X is mdpt. of AC. 1 2

ReasonsStatements

5. DX BX


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