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**Bell Work Wednesday, August 7, 2013**

List two acts that will results in a student having a teacher conference.

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Standard Congruency postulates, SSS, SAS, ASA, & AAS

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Essential Question How does learning the congruency postulates help me prove that two triangle are congruent?

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Closing See nature by numbers video: Homework Assignment #1 – You saw the video, Nature by Numbers. Submit a picture of something from nature and point out one or several geometric shapes similarly to what you saw in the video. Due: Thursday in class.

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**The congruence postulates: SSS, SAS, ASA, & AAS**

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**Proving Triangles Congruent**

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**The Idea of a Congruence**

Two geometric figures with exactly the same size and shape. A C B D E F

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

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Corresponding Parts You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. B A C AB DE BC EF AC DF A D B E C F ABC DEF E D F

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

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Side-Side-Side (SSS) AB DE BC EF AC DF ABC DEF B A C E D F

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**Side-Angle-Side (SAS)**

B E F A C D AB DE A D AC DF ABC DEF included angle

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Included Angle The angle between two sides H G I

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**Included Angle Name the included angle: YE and ES ES and YS YS and YE**

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**Angle-Side-Angle (ASA)**

B E F A C D A D AB DE B E ABC DEF included side

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Included Side The side between two angles GI GH HI

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**Included Side Name the included side: Y and E E and S S and Y YE**

ES SY

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**Angle-Angle-Side (AAS)**

B E F A C D A D B E BC EF ABC DEF Non-included side

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**There is no such thing as an SSA postulate!**

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

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**There is no such thing as an AAA postulate!**

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

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**The Congruence Postulates**

SSS correspondence ASA correspondence SAS correspondence AAS correspondence SSA correspondence AAA correspondence

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Name That Postulate (when possible) SAS ASA SSA SSS

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Name That Postulate (when possible) AAA ASA SSA SAS

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**Name That Postulate SAS SAS SSA SAS Vertical Angles Reflexive Property**

(when possible) Vertical Angles Reflexive Property SAS SAS Vertical Angles Reflexive Property SSA SAS

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**HW: Name That Postulate**

(when possible)

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**HW: Name That Postulate**

(when possible)

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**Let’s Practice B D AC FE A F**

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

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

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**Write a congruence statement for each pair of triangles represented.**

B D A C E F

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Slide 1 of 2 1-1A

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Slide 1 of 2 1-1B

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5.6 ASA and AAS

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**Before we start…let’s get a few things straight**

C X Z Y INCLUDED SIDE

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**Angle-Side-Angle (ASA) Congruence Postulate**

Two angles and the INCLUDED side

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**Angle-Angle-Side (AAS) Congruence Postulate**

Two Angles and One Side that is NOT included

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**Your Only Ways To Prove Triangles Are Congruent**

SSS SAS ASA AAS Your Only Ways To Prove Triangles Are Congruent

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**Alt Int Angles are congruent given parallel lines**

Things you can mark on a triangle when they aren’t marked. Overlapping sides are congruent in each triangle by the REFLEXIVE property Alt Int Angles are congruent given parallel lines Vertical Angles are congruent

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Ex 1 DEF NLM

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Ex 2 What other pair of angles needs to be marked so that the two triangles are congruent by AAS? F D E M L N

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Ex 3 What other pair of angles needs to be marked so that the two triangles are congruent by ASA? F D E M L N

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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 4 G I H J K ΔGIH ΔJIK by AAS

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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. B A C E D Ex 5 ΔABC ΔEDC by ASA

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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 6 E A C B D ΔACB ΔECD by SAS

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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 7 J K L M ΔJMK ΔLKM by SAS or ASA

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Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible. Ex 8 J T L K V U Not possible

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Slide 2 of 2 1-2A

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Slide 2 of 2 1-2B

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Slide 2 of 2 1-2B

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Slide 2 of 2 1-2C

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(over Lesson 5-5) Slide 1 of 2 1-1A

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(over Lesson 5-5) Slide 1 of 2 1-1B

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Slide 1 of 2 1-1A

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Slide 1 of 2 1-1B

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Slide 1 of 2 1-1B

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Slide 1 of 2 1-1C

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Slide 2 of 2 1-2A

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Slide 2 of 2 1-2A

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Slide 2 of 2 1-2A

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Slide 2 of 2 1-2A

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