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Geometry Unit 2 Proofs

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• 2.1 warm up
• 2.1 opener cont.
• 2.2 opener
• 2.3 opener
• 2.3
• 2.4 opener
• ### Proofs

1. 1. True or False? Why?1. If you are in Guangdong, you are in China.2. If you are in China, then you are in Guangdong.3. If you are in Shekou, then you are in Guangdong.4. If you are in Guangdong, then you are in Shekou.
2. 2. True or False? Why?1. If an animal is a beagle, then it is a dog. Animals2. If animal is a dog, then it is a beagle. Dogs3. All animals are dogs.4. All dogs are animals. Beagles5. Draw a Venn diagram that shows that all robins are birds, but not all birds are robins.
3. 3. Logic & Reasoning Foldable Half Half
4. 4. Logic & Reasoning Foldable 42 mm
5. 5. Logic & Reasoning Foldable Title/Name Conditional Statement Converse Inverse Contrapositive Biconditional
6. 6. Logic & Reasoning Foldable Title/Name Definition Example True or False? Symbolic FormConditional CounterexampleStatement (2.1) Converse (2.1) Inverse (2.1)Contrapositive (2.1)Biconditional (2.2)
7. 7. Conditional:Made up of hyp. & concl.Uses if..., then … Or …only if…Two points are collinear only if they are on the same line.ORIf two points are http://www.cartoonstock.com/directory/c/conditional_offer.asp collinear, then they are on the same line.
8. 8. Converse:Switch hyp. & concl. http://www.free-extras.com/search/1/converse+batman+begins.htmIf two points are on the same line, then they are collinear.
9. 9. Inverse:Negate both hyp. & concl. of cond.If two points are not collinear, then they are not on the same line. http://www.maniacworld.com/inverse-mohawk.html
10. 10. Contrapositive: Negate both hyp. & concl. Of converse If two points are not on the same line, then they are not collinear.
11. 11. Biconditional:Conditional + converse Both must be true!  If two points are collinear, then they are on the same line.  If two points are on the same line, then they are collinear.= Two points are collinear if and only if they are on the same line.
12. 12. Create your own At your table:  Write a conditional statement based on a school rule.  Create the converse, inverse, contrapositive and biconditional statements using the cutouts.  Determine if statements are true or false. ○ If false, provide a counterexample.
13. 13. What’s the converse?1. If M is the midpoint of AB, then AM=AB.  If AM=AB, then M is the midpoint of AB.
14. 14. Logic & Reasoning Foldable Symbolic Form Law of Law of Title/Name & How to read it Detachment Syllogism Conditional Statement (2.1) Definition Definition Converse (2.1) Inverse Example Example (2.1) Contrapositive (2.1) Biconditional (2.2)
15. 15. Five sisters all have their birthday in a different month and each on a different day of the week. Using the clues below, determine the month and day of the week each sisters birthday falls. 1. Paula was born in March but not on Saturday. Abigails birthday was not on Friday or Wednesday. 2. The girl whose birthday is on Monday was born earlier in the year than Brenda and Mary. 3. Tara wasnt born in February and her birthday was on the weekend. 4. Mary was not born in December nor was her birthday on a weekday. The girl whose birthday was in June was born on Sunday. 5. Tara was born before Brenda, whose birthday wasnt on Friday. Mary wasnt born in July.
16. 16. Need Help?
17. 17. Put the steps in order. Describe why. 1. 10y + 5 - 5 = 25 - 5 2. y=2 3. 10y = 20 4. 10y = 20 10 10 http://www.electrical-picture.com/inductive-vs-deductive-reasoning/ 5. 10y + 5 = 25
18. 18. PropertiesProperty DefinitionAddition Property If a=b, then a+c=b+cSubtraction Property If a=b, then a-b=b-cMultiplication Property If a=b, then ac=bcDivision Property If a=b and c=0, then a/c=b/cDistributive Property a(b+c)=ab+ac
19. 19. Properties Reflexive Property  a=a http://www.earblessings.com/2010/06/twin-shadow-castles-in-snow.htmlhttp://www.photoshopessentials.com/photo-effects/water-reflection/
20. 20. Properties Symmetric Property  If a=b, then b=a http://www.cristinacabal.com/?p=373
21. 21. Properties Transitive Property  If a=b and b=c, then a=c http://www.buzzfeed.com/iloverobots