Unit 2: CSI Geometry: Logic and Reasoning

Transcription

1 Unit 2: CSI Geometry: Logic and Reasoning Standard Focus: Geometry and Spatial Sense Time Range : 1-3 Days Supplies : Pencil and Paper Topics of Focus : - Logic and Conjectures - Compound Statements - Venn Diagrams - Deductive Reasoning This particular was mapped to the Logic and Reasoning curriculum of most geometry textbooks and can be used as an enrichment or review activity. Congruence Congruence Congruence G-CO G-CO G-CO 9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. 10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. 11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

2 CSI Geometry: Logic & Reasoning Detectives, What s another month without a series of high profile robberies at the hands of the Mathemagicians? The evil genius terrorist group has pulled off another elaborate crime spree that has left the country of France in disarray. As the Mathemagicians work to build their world conquering device, our investigators are trying to piece together the thefts by an anonymous associate, Quasi Truthful. Cocky as always, the Mathemagicians have left behind a trail of mathematical puzzles and a cryptic text message that must be solved. After solving the puzzles, you can decode the message which will lead to Quasi s favorite number. So far there are six suspects that police have questioned. It is hoped that someone with relatively strong geometry and reasoning skills can crack the codes that have puzzled the detectives on the case so far. Since you are being brought in as a specialist you have to have definitive proof in order for any arrest to hold up in court. You need to be prepared to state your case and demonstrate your understanding of the following skills that Quasi is known to use in the notes. - Logic and Conjectures - Compound Statements - Venn Diagrams - Deductive Reasoning Be sure to include: - Other examples of the concepts - Definitions - Any other relevant information. Keep in mind, the slightest miscalculation or illegible footnote could result in a not guilty verdict. Oh, did I mention that use of a calculator might prematurely set off his world conquering device? Good luck to you, gumshoe. Chief Harris

3 Who is Quasi Truthful? Name: Marie Occupation: Hairdresser Favorite Number: -21 Name: Aminata Occupation: Restaurant Owner Favorite Number: 0 Name: Coco Occupation: Trust Fund Baby Favorite Number: 97 Name: Jessica Occupation: Musician Favorite Number: 44 Name: Napoleon XI Occupation: Pizzeria Owner Favorite Number: 11 Name: Napoleon XII Occupation: Pizza Boy Favorite Number: 12

4 Scene #1 Eiffel Tower - Paris, France In the middle of the night, Quasi Truthful helicoptered in and stole the top deck to the Eiffel Tower. In its place, investigators found this note. Bonjour, I m sure some will be salty that I stole the top of the Eiffel Tower. Others will be salty about this geometric proof. Prepare yourselves for a lot more French style sodium chloride-ness (SALT!) Plug in the correct definitions or properties. (You will use one more than once) Given: EG FH, BE DF Prove: BG DH 1. EG FH, BE DF EG = FH, BE = DF EG + BE = FH + DF BG = EG + BE, DH = FH + DF BG = DH BG DH 6. Which one is leftover? This will give you your first clue. Addition Property f = 1 Transitive Property a = 3 Given c = 5 Substitution r = 2 Def. of Congruent Segments n = 4 Segment Addition Postulate e = 6 The leftover = Scene #2 The Louvre - Paris, France Investigators believe that Quasi dug a tunnel into the Louvre and stole the legs from the Venus de Milo. Someone already stole the arms, so I had to go for the legs. Let s see what kind of deductive skills you have. The four tourists below went to four different landmarks around France. See if you can figure out who went where with just three clues. CLUE 1: Emma, Felix and Clara visited landmarks where they could go inside a structure. CLUE 2: A man took a picture of a landmark with a glass pyramid. CLUE 3: Nate and Emma visited landmarks outside of Paris. The first letter of the person s name who went to the Arc de Triumph is equal to -5. Palace of Versailles Dune of Pyla Arc de Triumph Louvre Clara Nate Emma Felix = -5

5 Scene #3 Les Invalides -- Paris, France The Museum of French Military History was rocked with cannon fire and Quasi Truthful escaped with two replica guillotines. I wanted to rob the Bastille, but I found out it was torn to the ground! Saltiness! Anywho, I stumbled into this museum. Great military leaders have to do multiple things correctly at one time. Whoever is truthful for both p and q will lead you to your next clue. Military Leader (p) Angle 1 is equal to 35 (q) My statement is always true If p q are true My Clue for You Joan of Arc m 1 = 5x + 10 m 2 = 30x 5 If AB = BC then B must be the midpoint of AC. Charlemange m 1 = 9x + 8 m 2 = 10x If two congruent angles are supplementary then they are right angles. Charles de Gauille m 1 = -2x + 21 m 2 = 6x + 37 Through any two points, there is exactly one line. Napoleon m 1 = 7x + 28 m 2 = 63 8x If two planes intersect, then their intersection is a point. The correct clue =

6 Scene #4 Château d'if - Frioul Archipelago, France Quasi Truthful sailed over to the famed prison fortress and made off with 16,000 pounds of stone. Carved into a cell, investigators found this note: I really have ~(enjoyed) spending this time with you. I m sure you are ~(not salty) by now. I think you have a ~(great) chance of catching me. ~(Good) Luck. Before England stole the idea with Sherlock Holmes, C. Auguste Dupin and Monsieur Lecoq were the first real fiction detectives. They could analyze cases and smell the truth. Can you? Use the statements and find the conjunction or disjunction that is true. (You may need to check your literature book) p q r s The Three Musketeers are named Athos, Porthos and Thanos Quasimodo was an underdog halfback on the Notre Dame Football Team The Man in the Iron Mask and the Count of Monte Cristo are brothers Ratatouille was based on a true story p (r q) (q s ) ~r q (~p ~s) (~r q) p Which is true?... = Scene #5 Mirazur - Menton, France A discarded supply of mutated oysters were found to be picked out of the trash. While it s unclear how these oysters may factor into the world conquering device, Quasi Truthful left this note. While my French is a little rusty, I m pretty sure they like cheese. After the appetizer and entrée in a classic French meal, there is a course of cheese. 200 customers could choose any combination of three different cheeses. The results can be seen in the Venn diagram. How many people ate Camembert or Brie de Meaux, but did not eat any Roquefort cheese? The answer will be equal to r. r =

7 Scene #6 Axe Historique -- Paris, France French police were stunned to find all of the shrubs from the famed Axe Historique line of buildings and monuments were uprooted. Written in sidewalk chalk they found this note. Later, they were sent a cryptic text message. I might come back to visit France just for kicks! I ve had to spend so much time stealing stuff, I didn t get to stop and smell the roses. For the final puzzle Napoleon made a change to the French flag. Are the blue, white and red equal? Au revoir! Which proof is correct? Option Un By the definition of midpoint of a segment, AB = BC and BC = CD. By the transitive property, AB = CD. Therefore by the definition of congruence, if segments have the same measure then they are congruent. Thus, AB BC CD. Given: B is the midpoint of AC, C is the midpoint of BD. Prove: AB BC CD Option Deux Since B is a midpoint of a segment, by its definition, AB = BC and BC = CD. By the converse of the segment addition postulate this means the segments have the same measure. Therefore by the definition of congruence, AB BC CD. Which is correct?... = CRYPTIC PUZZLE SOLVER TEXT MESSAGE Haha. You salty. F (R + A) (N + C) + E Quasi ~(Truthful)