10/20/2011Keystone Geometry Proving Parts of Triangles using CPCTC.

Slides:

Advertisements

Similar presentations

Proving Triangles Congruent

Advertisements

4-4 Using Congruent Triangles: CPCTC

CCGPS Analytic Geometry

Proving Triangles Congruent

1 MM1G3c Proving Triangles Congruent (AAS, HL). 2 Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding.

Blue – 3/9/2015 Gold – 3/10/2015.  Last 2 classes, we talked about 3 ways we can determine triangle congruence.  CPCTC – All 3 sides and 3 angles of.

Proving Triangles Congruent Geometry D – Chapter 4.4.

Proving Triangles Congruent: SSS and SAS

4.6 Using Congruent Triangles

4-4 & 4-5: Tests for Congruent Triangles

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

Chapter 4 Congruent Triangles.

1Geometry Lesson: Isosceles and Equilateral Triangle Theorems Aim: What theorems apply to isosceles and equilateral triangles? Do Now: C A K B Given: Prove:

Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Aim: Do Now: How do we prove overlapping triangles are congruent?

EXAMPLE 1 Identify congruent triangles Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or.

Proving Triangles are Congruent (NOTES)

4.6 Using Congruent Triangles

Proving Triangles Congruent. Steps for Proving Triangles Congruent 1.Mark the Given. 2.Mark … reflexive sides, vertical angles, alternate interior angles,

Exploring Congruent Triangles. Congruent triangles: Triangles that are the same size and shape – Each triangle has six parts, three angles and three sides.

Holt Geometry 4-6 Triangle Congruence: CPCTC Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ?. 2. What is the distance between (3, 4) and (–1, 5)? 3.

Lesson 7.1 Right Triangles pp

Unit 4 Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL)

Holt Geometry 4-6 Triangle Congruence: CPCTC 4-6 Triangle Congruence: CPCTC Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.

1Geometry Lesson: Pairs of Triangles in Proofs Aim: How do we use two pairs of congruent triangles in proofs? Do Now: A D R L B P K M.

Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ?. 2. What is the distance between (3, 4) and (–1, 5)? 3. If 1  2, why is a||b? 4. List methods used.

Triangle Congruences SSS SAS AAS ASA HL.

Proving Congruence – SSS, SAS Side-Side-Side Congruence Postulate (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then.

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Triangle Congruence by SSS & SAS Objective: To Determine whether triangles are congruent using SSS and SAS postulate.

Using Congruent Triangles Part 1 Keystone Geometry 11/08/2013.

Chapter 4 Review Cut-n-Paste Proofs. StatementsReasons SAS Postulate X is midpoint of AC Definition of Midpoint Given Vertical Angles Theorem X is midpoint.

Using Special Quadrilaterals

Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ? .

Advanced Geometry 3.3. Objective To write proofs involving congruent triangles and CPCTC.

4.4 Proving Congruence – SSS and SAS What you’ll learn: 1.To use SSS Postulate to test for triangle congruence. 2.To use the SAS Postulate to test for.

Geometry Worksheets Congruent Triangles #3.

4-4 Using Corresponding Parts of Congruent Triangles I can determine whether corresponding parts of triangles are congruent. I can write a two column proof.

Warm Up Check homework answers with each other!. Ch : Congruence and Triangles Students will prove triangles congruent using SSS, SAS, ASA, AAS,

Triangle Proofs. USING SSS, SAS, AAS, HL, & ASA TO PROVE TRIANGLES ARE CONGRUENT STEPS YOU SHOULD FOLLOW IN PROOFS: 1. Using the information given, ______________.

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Chapters 2 – 4 Proofs practice. Chapter 2 Proofs Practice Commonly used properties, definitions, and postulates  Transitive property  Substitution property.

Using Triangle Congruence to Prove Sides and Angles Congruent C h. 5-2

4-8 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?

Proving Triangles Congruent

Objective! Use CPCTC to prove parts of triangles are congruent.

Proving Triangles Congruent

Warm Up (on the ChromeBook cart)

Three ways to prove triangles congruent.

Proving Parts of Triangles using CPCTC

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-6 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Two-Column Triangle Proofs

Ways to Prove Triangles Congruent

Objective! Use CPCTC to prove parts of triangles are congruent.

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-2 Some Ways to Prove Triangles Congruent (p. 122)

K Aim: Do Now: How do we prove overlapping triangles are congruent? State the names of two triangles in each diagram: 2) F M B R H 1) A B C D 3)

Aim: Do Now: ( ) A B C D E Ans: S.A.S. Postulate Ans: Ans:

Geometry Proofs Unit 12 AA1.CC.

CPCTC uses congruent triangles to prove corresponding parts congruent.

8.3 Methods of Proving Triangles Similar

Ex: Given: Prove: CPCTC:

Ways to prove triangles congruent:

4-2 Triangle congruence by sss & sas

Basic Geometry Section 4-6: Triangle Congruence: CPCTC

Presentation transcript:

10/20/2011Keystone Geometry Proving Parts of Triangles using CPCTC

Proof Format When using CPCTC to prove that corresponding parts of a triangle are congruent, we use the same general format: –Determine the 3 pieces of congruency based on the given information and the diagram –Determine what the two congruent triangles are and the method of congruence –Use CPCTC to prove the corresponding parts. When using CPCTC to prove that corresponding parts of a triangle are congruent, we use the same general format: –Determine the 3 pieces of congruency based on the given information and the diagram –Determine what the two congruent triangles are and the method of congruence –Use CPCTC to prove the corresponding parts.

Complete the following proof: StatementsReasons 1.DF bisects <EDG DE = DG 2. <1 = <2 3. DF = DF 4. ∆ = ∆ 5.

Complete the following proof: StatementsReasons 1. PR=SR; PQ=SQ1. Given 2. QR=QR2. Reflexive 3. ∆PQR= ∆SQR3. SSS Postulate 4. <P=<S4. CPCTC

Complete the following proof: StatementsReasons 1. C is the midpoint of AD; <A=<D 1. Given 2. AC=CD2. Def. of a Midpt. 3. <ACB=<DCE3. Vertical Angles 4. ∆ABC= ∆DEC4. ASA Postulate 5. BC=EC5. CPCTC

Complete the following proof: StatementsReasons 1. WY is perp. To XZ; XY=YZ 1. Given 2. <XYW=<ZYW2. If 2 lines are perp. Then they form = adj. <s 3. WY=WY3. Reflexive 4. ∆XYW= ∆ZYW4. SAS Postulate 5. <X=<Z5. CPCTC