Geometry Proofs Unit 12 AA1.CC.

Slides:

Advertisements

Similar presentations

4-4 Using Congruent Triangles: CPCTC

Advertisements

CCGPS Analytic Geometry

Chapter 9 Geometry © 2008 Pearson Addison-Wesley. All rights reserved.

Using Congruent Triangles Geometry Mrs. Spitz Fall 2004.

Section 9-3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.

SECTION 4.4 MORE WAYS TO PROVE TRIANGLES CONGRUENT.

Lesson: Pages: Objectives: 4.3 Exploring CONGRUENT Triangles 196 – 197  To NAME and LABEL Corresponding PARTS of CONGRUENT Triangles  To STATE the CPCTC.

Module 5 Lesson 2 – Part 2 Writing Proofs

& 5.2: Proving Triangles Congruent

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 9-4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.

Section 5-2 Bisectors in Triangles. Vocabulary Distance from a point to a line: the length of the perpendicular segment from the point to the line.

Given: DB bisects AE

Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 3.1 Congruent Triangles.

Give reasons for each step in this proof. B D A E C Given: C is the midpoint of AC, C is the midpoint of DB Prove: AB is congruent to ED StatementsReasons.

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.

Holt McDougal Geometry 4-Ext Proving Constructions Valid 4-Ext Proving Constructions Valid Holt Geometry Lesson Presentation Lesson Presentation Holt McDougal.

4.1 – 4.3 Triangle Congruency Geometry.

4.4 Isosceles Triangles, Corollaries, & CPCTC. ♥Has at least 2 congruent sides. ♥The angles opposite the congruent sides are congruent ♥Converse is also.

Proving Congruent Triangles: SSS & SAS Ch 4 Lesson 3.

 If three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.  If AB = DE, BC = EF, AC.

Lesson 4 – 3 Congruent Triangles

Then/Now You identified and used congruent angles. Name and use corresponding parts of congruent polygons. Prove triangles congruent using the definition.

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.

5.2 Proving Triangles are Congruent: SSS and SAS Textbook pg 241.

Solve for x and y: 43° 75° y° x° 75° = y + 43° 75 – 43 = y 32° = y z° x and 43° are Alternate Interior Angles 43° = x.

Isosceles Triangles, Corollaries, & CPCTC

4.5 Proving Triangles Congruent - ASA and AAS

 ABC  DEF SSS AND SAS CONGRUENCE POSTULATES

7-3 Triangle Similarity I CAN -Use the triangle similarity theorems to

Warm Up m<L = m<L = 180 m<L =

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

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

6-2 Properties of Parallelograms

Proving Triangles Congruent

G.6 Proving Triangles Congruent Visit

Proving Triangles Congruent

Vocabulary Corollary Base angles Vertex angles.

Section 4-3 Congruent Triangles

Chapter 2.6 (Part 1): Prove Statements about Segments and Angles

4-3: Congruent Triangles

Prove Triangles Congruent by ASA & AAS

Congruent Triangle Proofs

 ABC  DEF SSS AND SAS CONGRUENCE POSTULATES

2. Definition of congruent segments AB = CD 2.

Ways to Prove Triangles Congruent

3.5 Overlapping Triangles

Proving Triangles Congruent

Similarity, Congruence, & Proofs

Lessons 4-4 and 4-5 Proving Triangles Congruent.

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

Congruent Triangle Shortcuts

Chapter 4.2 Notes: Apply Congruence and Triangles

Class Greeting.

Check Homework.

5.1 Congruence and Triangles Day 2

Proving Triangles Congruent

G.6 Proving Triangles Congruent Visit

5-3 Congruence Postulates for Triangles

Congruent Triangles.

Bell Work Complete problems 8, 9, and 15 from yesterday. Proofs are on the board.

 ABC  DEF SSS AND SAS CONGRUENCE POSTULATES

5.3 Congruent Triangles & Proof

Postulates and Theorems to show Congruence SSS: Side-Side-Side

Ex: Given: Prove: CPCTC:

DRILL Prove each pair of triangles are congruent.

2-6 Prove Statements About Segments and Angles

4.4 Prove Triangles Congruent by SAS and HL

Chapter 5 Congruent Triangles.

 ABC  DEF SSS AND SAS CONGRUENCE POSTULATES

Presentation transcript:

Geometry Proofs Unit 12 AA1.CC

Review: algebraic proof Statement Reason 5(x – 1) = 20 1. 2. 3. 4. x = 5 4.

Example1: Proving Congruence B D E C Given: CE = ED, AE = EB Prove: STATEMENTS REASONS 1. CE = ED Given 2. 2. Definition of ≅ segments 3. AE = EB 3. 4. 𝐴𝐸 ≅ 𝐸𝐵 4. 5. 5. Vertical Angles Theorem

Example 2: Proving Congruence Given: Prove: A B D C STATEMENTS REASONS 1. 1. Given 2. 2. Given 3. 3. Reflexive property 4.

Example 3: Proving Congruence Given: 𝐴𝐷 ≅ 𝐶𝐷 , 𝐴𝐵 ≅ 𝐶𝐵 Prove: B A C D STATEMENTS REASONS 1. 1. Given 2. 𝐴𝐵 ≅ 𝐶𝐵 2. 3. 4.

If ∆𝐴𝐵𝐶≅∆𝐷𝐸𝐹, then what do you know about their sides and angles??? Their corresponding sides are congruent!!! Their corresponding angles are congruent!!! Sides: 𝐴𝐵 ≅ 𝐷𝐸 𝐵𝐶 ≅ 𝐸𝐹 𝐴𝐶 ≅ 𝐷𝐹 Angles: ∠A ≅ ∠D ∠B ≅ ∠E ∠C ≅ ∠F *This is ‘CPCTC’ – a reason we can use in a poof!!!!

Corresponding Parts of Congruent Triangles are Congruent. CPCTC If you can prove congruence using a shortcut, then you KNOW that the remaining corresponding parts are congruent. You can only use CPCTC in a proof AFTER you have proved congruence.

Example: Prove: AB ≅ DE 1. AC ≅ DF 2. ∠C ≅ ∠F 3. CB ≅ FE Statements Reasons B C 1. AC ≅ DF 2. ∠C ≅ ∠F 3. CB ≅ FE 4. ΔABC ≅ ΔDEF 5. AB ≅ DE D F E

Example A B E C D Given: As marked in diagram Prove: CE  DE Statements A  B AC  BD AEC  BED ΔAEC  ΔBED CE  DE Reasons 1. 2. 3. 4. 5.