Take papers from your folder and put them in your binder. Place your binder, HW and text on your desk. YOUR FOLDERS SHOULD BE EMPTY current EXCEPT FOR YOUR WARM UP PAPER and current day’s classwork Warm-up- silently please 1)read page 232. Answer in a complete sentence on your warm–up paper: what does CPCTC mean? 2)do pg. 230, # 11 Honors Geometry 14 Nov 2011

Objective Students will review congruency shortcuts and use CPCTC to prove congruency Students will view a powerpoint presentation, take notes and work independently and with their group to solve problems.

Homework due today none Homework due Nov. 15 P1- extension-pg. 224: 1-21 odds Pg. 229: 2 – 20 evens TEST- Nov 16/17 Study: constructions, isosceles triangle properties, triangle sum, triangle inequalities, triangle congruency shortcuts

Term Definition Example- add notation (conguency marks) SSS Congruence Shortcut If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent SAS Congruence Shortcut If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent SSADOES NOT guarantee congruency not a nice word if you spell it backwards = NO guaranteed congruency!!! Chapter 4 Triangles

Term Definition Example ASA Congruence Shortcut If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. SAA Congruence Shortcut If two angles and a non- included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent AAADOES NOT guarantee congruency Chapter 4 Triangles--

Proving Triangles Congruent

Two geometric figures with exactly the same size and shape. The Idea of a Congruence A C B DE F

How much do you need to know... need to know about two triangles to prove that they are congruent?

In previous lessons, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Corresponding Parts  ABC   DEF B A C E D F 1.AB  DE 2.BC  EF 3.AC  DF 4.  A   D 5.  B   E 6.  C   F

Do you need all six ? NO ! SSS SAS ASA AAS

Side-Side-Side (SSS) 1. AB  DE 2. BC  EF 3. AC  DF  ABC   DEF B A C E D F

Side-Angle-Side (SAS) 1. AB  DE 2.  A   D 3. AC  DF  ABC   DEF B A C E D F included angle

The angle between two sides Included Angle  G G  I I  H H

Name the included angle: YE and ES ES and YS YS and YE Included Angle SY E  E E  S S  Y Y

Angle-Side-Angle (ASA) 1.  A   D 2. AB  DE 3.  B   E  ABC   DEF B A C E D F include d side

The side between two angles Included Side GI HI GH

Name the included side:  Y and  E  E and  S  S and  Y Included Side SY E YE ES SY

Angle-Angle-Side (AAS) 1.  A   D 2.  B   E 3. BC  EF  ABC   DEF B A C E D F Non- included side

Warning: No SSA Postulate A C B D E F NOT necessarily CONGRUENT There is no such thing as an SSA postulate!

Warning: No AAA Postulate A C B D E F There is no such thing as an AAA postulate! NOT necessarily CONGRUENT

The Congruence Postulates  SSS correspondence  ASA correspondence  SAS correspondence  AAS correspondence  SSA correspondence  AAA correspondence

Name That Postulate SAS ASA SSS SSA (when possible)

Name That Postulate (when possible) ASA SAS AAA SSA

Name That Postulate (when possible) SAS SAS SAS Reflexive Property Vertical Angles Reflexive Property SSA take notes…

CW: Name That Postulate (when possible)

CW: Name That Postulate

Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS:  B   D For AAS: A  F A  F AC  FE

CW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

This powerpoint was kindly donated to is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.

Corresponding parts When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are, that means that ALL the corresponding parts are congruent. EX: If a triangle is congruent by ASA (for instance), then all the other corresponding parts are. A C B G E F That means that EG CB What is AC congruent to? FE

Corresponding parts of congruent triangles are congruent.

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

Prove: AB DE A FE D C B Statements Reasons AC DF Given ⦟ C ⦟ F Given CB FE Given ΔABC ΔDEF SAS AB DE CPCTC

EXAMPLE 2 Use the SAS Congruence Postulate CW: Write a proof. GIVEN PROVE STATEMENTS REASONS BC DA, BC AD ABC CDA 1. Given 1. BC DA S Given 2. BC AD 3. BCA DAC3. Alternate Interior Angles Theorem A 4. AC CA Reflexive Property of Congruence S

EXAMPLE 2 Use the SAS Congruence Postulate STATEMENTS REASONS 5. ABC CDA SAS Congruence Postulate 5.

debrief what did you learn today? what was easy? what was difficult? what can I do to help you?