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## Bell Work Tuesday, August 6, 2013

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**Bell WorkTuesday, August 6, 2013**List two acts that will results in a student going to ISS for one day.**Closing**• See nature by numbers video:http://www.youtube.com/watch?v=kkGeOWYOFoA • 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: Wednesday in class.**F**B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape.**How much do you**need to know. . . . . . about two triangles to prove that they are congruent?**Corresponding Parts**• AB DE • BC EF • AC DF • A D • B E • C F B A C E F D You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF**SSS**SAS ASA AAS Do you need all six ? NO !**Side-Side-Side (SSS)**E B F A D C • AB DE • BC EF • AC DF ABC DEF**Side-Angle-Side (SAS)**B E F A C D • AB DE • A D • AC DF ABC DEF included angle**Included Angle**The angle between two sides H G I**E**Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y**Angle-Side-Angle (ASA)**B E F A C D • A D • AB DE • B E ABC DEF included side**Included Side**The side between two angles GI GH HI**E**Y S Included Side Name the included side: Y and E E and S S and Y YE ES SY**Angle-Angle-Side (AAS)**B E F A C D • A D • B E • BC EF ABC DEF Non-included side**Warning: No SSA Postulate**There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT**Warning: No AAA Postulate**There is no such thing as an AAA postulate! E B A C F D NOT CONGRUENT**SSS correspondence**• ASA correspondence • SAS correspondence • AAS correspondence • SSA correspondence • AAA correspondence The Congruence Postulates**Name That Postulate**(when possible) SAS ASA SSA SSS**Name That Postulate**(when possible) AAA ASA SSA SAS**Name That Postulate**(when possible) Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SSA SAS**HW: Name That Postulate**(when possible)**HW: Name That Postulate**(when possible)**Let’s Practice**ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS:**HW**Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:**Write a congruence statement for each pair of triangles**represented. D B C A E F**1-1A**Slide 1 of 2**1-1B**Slide 1 of 2**5.6**ASA and AAS**C**Y A B X Z Before we start…let’s get a few things straight INCLUDED SIDE**Angle-Side-Angle (ASA) Congruence Postulate**A A S S A A Two angles and the INCLUDED side**A**A A A S S Angle-Angle-Side (AAS) Congruence Postulate Two Angles and One Side that is NOT included**SSS**SAS ASA AAS Your Only Ways To Prove Triangles Are Congruent**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**Ex 1**DEF NLM**D**L M F N E Ex 2 What other pair of angles needs to be marked so that the two triangles are congruent by AAS?**D**L M F N E Ex 3 What other pair of angles needs to be marked so that the two triangles are congruent by ASA?**G**K I H J 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 ΔGIH ΔJIK by AAS**B**A C D E 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 5 ΔABC ΔEDC by ASA**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**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**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**1-2A**Slide 2 of 2**1-2B**Slide 2 of 2**1-2B**Slide 2 of 2**1-2C**Slide 2 of 2**(over Lesson 5-5)**1-1A Slide 1 of 2**(over Lesson 5-5)**1-1B Slide 1 of 2**1-1A**Slide 1 of 2