Geometry 4-6 CPCTC C – Corresponding P – Parts of C – Congruent

Slides:

Advertisements

Similar presentations

1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Congruent Triangles Stage 6 - Year 11 Mathematic ( Preliminary )

Advertisements

6-2: Proving Congruence using congruent parts Unit 6 English Casbarro.

Chapter 4.6 Notes: Use Congruent Triangles Goal: You will use congruent triangles to prove that corresponding parts are congruent.

Unit 2 Part 4 Proving Triangles Congruent. Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles.

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.

By Shelby Smith and Nellie Diaz. Section 8-1 SSS and SAS  If three sides of one triangle are congruent to three sides of another triangle, then the triangles.

TODAY IN GEOMETRY…  REVIEW: SSS, SAS, HL, ASA, AAS  WARM UP: PROOF-A-RAMA 1  Learning Goal: 4.6 Use CPCTC to prove congruent parts of a triangle  Independent.

Geometry 4.3 Using Congruent Triangles. In yesterday’s lesson you learned how to prove two triangles congruent by SSS SAS ASA After we prove Δ’s …….today.

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

8.2 CPCTC Geometry.

Honors Geometry Section 4.3 cont. Using CPCTC. In order to use one of the 5 congruence postulates / theorems ( )we need to show that 3 parts of one triangle.

Isosceles Triangles, Corollaries, & CPCTC

Triangle Congruence Theorems

Prove triangles congruent by ASA and AAS

Geometry-Part 7.

Triangle Congruence Theorems

Proving Triangles are Congruent

Bell Ringer 10/21/

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

Sections 6.3 & 6.4 Proving triangles are similar using AA, SSS, SAS

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?

5.3 Proving Triangles are congruent:

Proving Triangles Congruent: SSS and SAS

4-2 Triangle Congruence by SSS and SAS

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

Other Methods of Proving Triangles Congruent

Proving Triangles Congruent

Three ways to prove triangles congruent.

Lessons 25, 28, 30, & 36: Proving Triangles Congruent

4-4 and 4-5: Congruent Triangle Theorems

Proving Triangles Similar

Congruent Triangle Proofs

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

4-5 Triangle Congruence: ASA, AAS & HL

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

4.5 ASA and AAS Ways to prove 2 triangles congruent:

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

5.7 Vocabulary CPCTC CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification.

Objective Use CPCTC to prove parts of triangles are congruent.

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

Triangle Congruence Theorems

Identifying types and proofs using theorems

CPCTC uses congruent triangles to prove corresponding parts congruent.

Geometry Unit 6 Name: _________________________

4-7 & 10-3 Proofs: Medians Altitudes Angle Bisectors Perpendicular

Proving Triangles Similar.

8.3 Methods of Proving Triangles Similar

SSS, SAS, ASA, & AAS Students will prove two triangles are congruent using the SSS, SAS, ASA, & AAS Postulates.

Proving Triangles Congruent

Isosceles/ Equilateral

Proving Triangles Similar.

Warmup Write a congruence statement for the triangles.

Similar Similar means that the corresponding sides are in proportion and the corresponding angles are congruent. (same shape, different size)

DRILL Prove each pair of triangles are congruent.

S O L R E V I W Proving ∆s Congruent Type notes here.

Proving Triangles are Congruent

Triangle Congruency Theorems (shortcuts)

CPCTC and Circles Advanced Geometry 3.3.

Warm Up 7.4 Is there enough information to prove that the triangles are congruent? If so, state the reason (SSS, SAS, HL, ASA,

4-4/4-5 Proving Triangles Congruent

Proving Triangles Congruent

SSS SAS AA How do you use corresponding sides and angles to determine the similarity of triangles?

8.3 Methods of Proving Triangles are Similar Advanced Geometry 8.3 Methods of Proving    Triangles are Similar Learner Objective: I will use several.

4-2 Triangle congruence by sss & sas

Basic Geometry Section 4-6: Triangle Congruence: CPCTC

4.2 /4.3 – Triangle Congruence

Module 16: Lesson 4 AA Similarity of Triangles

Notes 3.1 Congruent Triangles.

Presentation transcript:

Geometry 4-6 CPCTC C – Corresponding P – Parts of C – Congruent T – Triangles are After you prove two triangles are congruent using SSS, SAS, ASA, AAS, or HL Then you can say that all of their unmarked sides and angles are also congruent by CPCTC.

Example Determine if the two Δ’s are congruent. If they are, find the value of x. A U 3x-3 V C 24 T B ΔABC ≅ ΔTVU by HL. So, AB ≅ TV by CPCTC. 3x – 3 = 24 and x = 9.

Example Determine if the two Δ’s are congruent. If they are, find the value of x. 2x 3x - 4 You cannot use unmarked sides. So, there is not enough information to prove the two triangles are congruent.

Example Given: PR bisects QPS and QRS. Find the values of x and y. 125° 12 2y - 4 x - 5° ΔPRS ≅ ΔPRQ by ASA. PQ ≅ PS by CPCTC. 2y – 4 = 12 so y = 8. ∠Q ≅ ∠S by CPCTC. x – 5 = 125 so x = 130.