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Course: Geometry Chapter 2: Geometric Reasoning Big Idea: Study inductive and deductive reasoning. Use conditional and biconditional statements. Write two-column, flow and paragraph proofs. Learning Target: I CAN 2-1a … Use inductive reasoning to identify patterns and make conjectures Example Find the next item in the pattern. 1. 100, 81, 64, 49, … 2. Alabama, Alaska, Arizona, … Complete the conjecture. 3. The square of any negative number is: 4. The number of segments determined by n points is: 2-1b. … Find counterexamples to disprove conjectures Show that each conjecture is false by finding a counterexample. 1. For any integer n, n3 > 0 2. Each angle in a right triangle has a different measure 2-2a. … Identify, write and analyze the truth value of conditional statements 4.7 Identify the hypothesis and conclusion of the conditional. 1. If you can see the stars, then it is night. 2. A pencil writes well if it is sharp. 2-2b. … Write the inverse, converse and contrapositive of a conditional statement 2-3. … Apply the Law of Detachment and Law of Syllogism in logical reasoning Determine if each conditional is true. If false, give a counterexample. 3. If two points are collinear, then a right triangle contains one obtuse angle. 4. If a living thing is green, then it is a plant. Write the converse, inverse and contrapositive: If an animal is an armadillo, then it is nocturnal. Determine if the conjecture is valid by the Law of Detachment. 1. Given: An obtuse triangle has two acute angles. Triangle ABC is obtuse. Conjecture: Triangle ABC has two acute angles. Determine if the conjecture is valid by the Law of Syllogism. 2. Given: The radio is distracting when I am studying. If it is 7:30 PM on a weeknight, I am studying. Conjecture: If it is 7:30 PM on a weeknight, the radio is distracting. 3. Given: No human is immortal. Fido the dog is not human. Conjecture: Fido the dog is immortal. Starting Getting There Got It Learning Target: I CAN 2-4. … Write and analyze biconditional statements Example Starting Write the converse and a biconditional statement for the following: 1. Conditional: An angle is obtuse when it measures between 90o and 180o For the conditional, write the converse and a biconditional statement. 2. Conditional: If n is an odd number, then n-1 is divisible by 2. Write each definition as a biconditional. 3. A cube is a three-dimensional solid with six square faces. 2-5a. … Review properties of equality and use them to write algebraic proofs : Write the property demonstrated by each statement: 1. If a = b, then ac = bc 2. a(b + c) = ab + ac 2-5b…. Identify properties of equality and congruence Solve the equation. Show all steps and write a justification for each step. 3. t + 6.5 = 3t – 1.3 Write the property demonstrated by each statement: 1. If SPR MLN and MLN DGY , then SPR DGY 2. If ABC DEF , then DEF ABC Solve the problem. Write justifications for each step in your solution. 3. Solve for m<ZYX in terms of m<CBD. Given: XYZ ABC 2-6…. Write two column proofs BD is the angle bisector of <ABC. Write a two-column proof. 1. Given: The sum of the angle measures in a triangle is 180 o Prove: m<1 = m<3 + m<4 3 1 2-7…. Write flowchart and paragraph proofs Re-write the given proof as a flowchart and paragraph proof. 1. Given: 4 3 Prove: m<1 = m<2 1 1 Statements 1. <1 and < 4 are supplementary 2. 3. 4 3 1 2 4. m<1 = m<2 Reasons 1. Linear Pair Theorem 2. Given 3. Supps. Theorem 4.Def. of angles 2 3 2 4 4 Getting There Got It