Test Review: Geometry L2 Period 1 and 3 Test Date: Friday November 6

Transcription

1 Test Review: Geometry L2 Period 1 and 3 Test Date: Friday November 6 Things it would be a good idea to know: 1) All terms, definitions, properties, postulates, theorems from Unit 1 and Unit 2 2) How to apply all definitions, properties, and postulates. 3) How to write a conditional statement as a converse. 4) How to prove a statement false (counterexample) 5) How to write a bi-conditional 6) How to write a 2-column proof 7) All information from previous chapters. Test Outline Part I. Part II. Part III. Part IV. Part V. Part VI. Multiple Choice and True/False 10 Questions (20pts) Always, Sometimes, Never 5 Questions (10pts) Complete the postulate 5 postulates (10pts) Conditionals, Converses, Bi-conditional & Counterexamples 2 (10pts) Short Answers 4 questions (20pts) 3 proofs (1 Algebra, 1 segment, 1 angle) (30pts)

2 NAME DATE PERIOD 2-3 Study Guide and Intervention Conditional Statements If-Then Statements An if-then statement is a statement such as If you are reading this page, then you are studying math. A statement that can be written in if-then form is called a conditional statement. The phrase immediately following the word if is the hypothesis. The phrase immediately following the word then is the conclusion. A conditional statement can be represented in symbols as p q, which is read p implies q or if p, then q. Example 1: Identify the hypothesis and conclusion of the conditional statement. If hypothesis, then conclusion Example 2: Identify the hypothesis and conclusion. Write the statement in if-then form. You receive a free pizza with 12 coupons. If, then hypothesis conclusion Exercises Identify the hypothesis and conclusion of each conditional statement. 1. If it is Saturday, then there is no school. 2. If x 8 = 32, then x = If a polygon has four right angles, then the polygon is a rectangle. Write each statement in if-then form. 4. All apes love bananas. 5. The sum of the measures of complementary angles is Collinear points lie on the same line. Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. 7. If today is Wednesday, then yesterday was Friday. 8. If a is positive, then 10a is greater than a. Chapter 2 19 Glencoe Geometry

3 NAME DATE PERIOD 2-3 Study Guide and Intervention (continued) Conditional Statements Converse. If you change the hypothesis or conclusion of a conditional statement, you form a related conditionas. This chart shows the converse, and how it s related to a conditional statement. Symbols Formed by Example Conditional p q using the given hypothesis and conclusion If two angles are vertical angles, then they are congruent. Converse q p exchanging the hypothesis and conclusion If two angles are congruent, then they are vertical angles. Just as a conditional statement can be true or false, the related conditionals also can be true or false. A conditional statement always has the same truth value as its contrapositive, and the converse and inverse always have the same truth value. Exercises Write the converse, inverse, and contrapositive of each true conditional statement. Determine whether each related conditional is true or false. If a statement is false, find a counterexample. 1. If you live in San Diego, then you live in California. 2. If a polygon is a rectangle, then it is a square. 3. If two angles are complementary, then the sum of their measures is 90. Chapter 2 20 Glencoe Geometry

4 NAME DATE PERIOD 2-3 Skills Practice Conditional Statements Identify the hypothesis and conclusion of each conditional statement. 1. If you purchase a computer and do not like it, then you can return it within 30 days. 2. If x + 8 = 4, then x = If the drama class raises $2000, then they will go on tour. Write each statement in if-then form. 4. A polygon with four sides is a quadrilateral. 5. An acute angle has a measure less than 90. Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. 6. If you have five dollars, then you have five one-dollar bills. 7. If I roll two six-sided dice and sum of the numbers is 11, then one die must be a five. 8. If two angles are supplementary, then one of the angles is acute. 9. Write the converse, inverse, and contrapositive of the conditional statement. Determine whether each statement is true or false. If a statement is false, find a counterexample. If 89 is divisible by 2, then 89 is an even number. Chapter 2 21 Glencoe Geometry

5 NAME DATE PERIOD 2-6 Study Guide and Intervention Algebraic Proof Algebraic Proof A list of algebraic steps to solve problems where each step is justified is called an algebraic proof, The table shows properties you have studied in algebra. The following properties are true for any real numbers a, b, and c. Addition Property of Equality If a = b, then a + c = b + c. Subtraction Property of Equality If a = b, the a c = b c. Multiplication Property of Equality If a = b, then a c = b c. Division Property of Equality If a = b and c 0, then, =. Reflexive Property of Equality a = a Symmetric Property of Equality If a = b and b = a. Transitive Property of Equality If a = b and b = c, then a = c. Substitution Property of Equality Distributive Property If a = b, then a may be replaced by b in any equation or expression. a (b + c) = ab + ac Complete each proof. 1. Given: = 9 Prove: x = 3 2. Given: 4x + 8 = x + 2 Prove: x = 2 Exercises State the property that justifies each statement. 1. If m 1 = m 2, then m 2 = m If m 1 = 90 and m 2 = m 1, then m 2 = If AB = RS and RS = WY, then AB = WY. 4. If AB = CD, then AB = CD. 5. If m 1 + m 2 = 110 and m 2 = m 3, then m 1 + m 3 = RS = RS 7. If AB = RS and TU = WY, then AB + TU = RS + WY. 8. If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. Chapter 2 37 Glencoe Geometry

6 State Justifications State the property that justifies each statement. 1) If 80 = m A, then m A = 80. 2) If RS = TU and TU = YP, then RS = YP. 3) If 7x = 28, then x = 4. 4) If VR + TY = EN + TY, then VR = EN. 5) If m 1 = 30 and m 1 = m 2, then m 2 = 30. 6) If m 1 = m 2, then m 2 = m 1. 7) If m 1 = 90 and m 2 = m 1, then m 2 = 90. 8) If AB = RS and RS = WY, then AB = WY. 9) If AB = CD, then AB = CD. 10) If m 1 + m 2 = 110 and m 2 = m 3, then m 1 + m 3 = ) If AB = RS and TU = WY, then AB + TU = RS + WY. 12) If m 1 = m 2 and m 2 = m 3, then m 1 = m 3. 13) If m n, then n m.

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8 Algebraic/Geometric 2-Column Proofs 1) Given: 8x 5 = 2x + 1 Prove: x = 1 2) FINANCE The formula for simple interest is I = prt, where I is interest, p is principal, r is rate, and t is time. Given: I = prt I Prove: r pt 3) 4) 5) Given: HJ 7x 3; HI 2x 6; IJ 3x 3 Prove: HI 12 6) Given: m QWT 2 x; m TWX x 6 Prove: m QWT 56 7) Given: ABC, CBD are supplementary. m ABC = 3x 5, and m CBD = Prove: x 52 8) Given: AB is an angle bisector of CAD. m BAC 7x 2, m BAD 5( x 4) Prove: m BAC 65