Geometry Unit 2 Review Day 1 What to expect on the test:

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1 Geometry Unit 2 Review Day 1 What to expect on the test: Conditional s Converse Inverse Contrapositive Bi-conditional statements Today we are going to do more work with Algebraic Proofs Counterexamples/Instances Converse of parallel lines conjecture Algebraic proofs and their properties Geometric proofs Name the Property of Equality (PoE) that justifies each statement. *If a = b, then b = a H. Symmetric PoE *xy = xy I. Reflexive PoE A. Addition PoE B. Subtraction PoE C. Multiplication PoE D. Division PoE E. Distributive PoE F. Substitution PoE G. Transitive PoE H. Symmetric PoE I. Reflexive PoE *If A = C and M = E, then A+M = C+E A. Addition PoE

2 Name the Property of Equality (PoE) that justifies each statement. *If A + B = 90 and A = 30, then 30 + B = 90 F. Substitution PoE *x + 3 = 17, then x = 14 B. Subtraction PoE A. Addition PoE B. Subtraction PoE C. Multiplication PoE D. Division PoE E. Distributive PoE F. Substitution PoE G. Transitive PoE H. Symmetric PoE I. Reflexive PoE *If 7x = 42, then x = 6. D. Division PoE Name the Property of Equality (PoE) that justifies each statement. *2(x + 4) = 2x + 8 E. Distributive PoE *If x = y + 3 and y + 3 = 10, then x = 10. A. Addition PoE B. Subtraction PoE C. Multiplication PoE D. Division PoE E. Distributive PoE F. Substitution PoE G. Transitive PoE H. Symmetric PoE I. Reflexive PoE G. Transitive PoE *Suppose Abdi's height = Juan's height and Juan's height = Marissa's height, then Abdi's height = Marissa's height. G. Transitive PoE

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5 Name the PoE that justifies each statement Name the PoE that justifies each statement

6 Name the PoE that justifies each statement Name the PoE that justifies each statement

7 Fill in the reasons and name the PoE that justifies each statement Conditional s: If a polygon is a hexagon, then it has six sides. Write the converse. Is it true or false? Write the inverse. Is it true or false? Write the contrapositive. Is it true or false? Write it as a bi conditional statement.

8 What are the three undefined terms in geometry? Why are they undefined? What's the difference between an axiom (postulate), definition, and theorem?

9 Euclid (a famous and very influential mathematician) began the study of Geometry by making statements such as: A straight line can be drawn between any two points. No one is able to prove this so they just accept it to be true. Is this statement a theorem or an axiom(postulate)? Explain your reasoning. Multiple Choice: Decide which of the following sketches of triangle ABC depicts an instance and which one shows a counterexample for the following statement. Provide one answer for the instance and one answer for the counterexample. Instance Counterexample

10 Find a counterexample to the statement: If two angles are complementary, then the angles are both 45 o. The square of a number is larger than that number If a polygon has four sides, then it is a square. If you live in Minnesota, then you live in Minneapolis. Are lines p and q parallel? 78 o p 102 o q

11 Which lines are // if... Geometric proof #1 t a b What do you see? Math? Two-Column Proof

12 Geometric proof #2 P C I G O W What do you see? Math? Two-Column Proof Geometric proof #2 Answer 1. Given 2. Definition of congruent angles Angle Addition Postulate Substitution PoE 5. Subtraction PoE 6. Definition of congruent angles

13 Good luck on your test! You WILL do great!