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day3chapter4.notebook November 03, 2015 Classwork: p. 248251, # 1323 (odd), 2429, 3133, 37, 39, 49 CHECK EVEN NUMBERS & 49 4.3 Congruent Triangles 1 day3chapter4.notebook November 03, 2015 If two geometric figures have the same shape and size, what can we say? THEY ARE CONGRUENT For a polygon to be congruent, all of it's corresponding parts must be congruent. What parts am I talking about? ANGLES AND SIDES CONGRUENT POLYGONS Definition: foldable 2 day3chapter4.notebook November 03, 2015 foldable Corresponding Parts (matching parts) "if and only if" conditional and converse are true If two polygons (we will deal mostly with triangles) are congruent, then their corresponding parts are congruent. CORRESPONDING PARTS OF CONGRUENT TRIANGLES ARE CONGRUENT OR CPCTC 3 day3chapter4.notebook November 03, 2015 C.P.C.T.C. foldable corresponding parts of congruent triangles are congruent Given: ABC XYZ X A Prove: BC YZ C Statements Reasons 1. 1. Given ABC XYZ B Z Y 2. BC YZ 2. CPCTC 4 day3chapter4.notebook November 03, 2015 3. 5 day3chapter4.notebook November 03, 2015 4. Since every triangles' inner angles must equal 180, then the following theorem must be true. THIRD ANGLES THEOREM If 2 angles of 1 triangle are congruent to 2 angles of a 2nd triangle, then the 3rd angle of both triangles are congruent. A J K C B If and L , then 6 day3chapter4.notebook November 03, 2015 6. 5. Properties of Triangle Congruence H C REFLEXIVE G I F A SYMMETRIC If B D , then E TRANSITIVE If and then 7 day3chapter4.notebook November 03, 2015 TwoColumn Proofs DO NOW Statements Reasons Do Statements Reasons 8 day3chapter4.notebook November 03, 2015 Homework: p. 257260 # 917 (odd), 18,19,20, 23, 24, 28, 29, 30,39 Down in the Cellar The Problem: In your cellar there are three light switches in the OFF position. Each switch controls 1 of 3 light bulbs on floor above. You may move any of the switches but you may only go upstairs to inspect the bulbs one time. How can you determine the switch for each bulb with one inspection?? The Solution: Number the switches 1, 2 & 3. Switch on number 1 for 1 minute, then switch it off. Switch on number 2. Go upstairs... The light that is on is connected to switch 2. The light that is off and warm is connected to switch 1. The light that is off and cold is connected to switch 3!! 9 day3chapter4.notebook November 03, 2015 10
