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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:http://www.youtube.com/watch?v=kkGeO WYOFoAhttp://www.youtube.com/watch?v=kkGeO WYOFoA 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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Two geometric figures with exactly the same size and shape. The Idea of a Congruence A C B DE F

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

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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

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

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

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

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The angle between two sides Included Angle G I H

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

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Angle-Side- Angle (ASA) 1. A D 2. AB DE 3. B E ABC DEF B A C E D F included side

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The side between two angles Included Side GI HI GH

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

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

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

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Warning: No AAA Postulate A C B D E F There is no such thing as an AAA postulate! 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 SAS ASA SSS SSA (when possible)

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Name That Postulate (when possible) ASA SAS AAA SSA

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

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HW: Name That Postulate (when possible)

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HW: Name That Postulate

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Lets 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 AC FE

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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. A B F C E D

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1-1A Slide 1 of 2

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1-1B Slide 1 of 2

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Before we start…lets get a few things straight INCLUDED SIDE AB C XZ Y

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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

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Overlapping sides are congruent in each triangle by the REFLEXIVE property Vertical Angles are congruent Alt Int Angles are congruent given parallel lines Things you can mark on a triangle when they arent marked.

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Ex 1 DEFNLM

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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. ΔGIH ΔJIK by AAS G I H J K Ex 4

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ΔABC ΔEDC by ASA BA C ED Ex 5 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.

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ΔACB ΔECD by SAS B A C E D Ex 6 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.

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ΔJMK ΔLKM by SAS or ASA JK L M Ex 7 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.

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Not possible K J L T U Ex 8 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. V

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1-2A Slide 2 of 2

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1-2B Slide 2 of 2

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1-2B Slide 2 of 2

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1-2C Slide 2 of 2

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

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

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1-1A Slide 1 of 2

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1-1B Slide 1 of 2

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1-1B Slide 1 of 2

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1-1C Slide 1 of 2

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1-2A Slide 2 of 2

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1-2A Slide 2 of 2

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1-2A Slide 2 of 2

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1-2A Slide 2 of 2

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