Number of Customers Geometry Honors Name: Chapter 2 Test Review 1. Based on the pattern, what are the next two terms of the sequence? 8, 15, 22, 29,... 2. Based on the pattern, what is the next figure in the sequence? 3. What conjecture can you make about the thirteenth term in the pattern A, B, A, C, A, B, A, C? 4. Laisha s Internet Services designs web sites and recently began a weekly advertising campaign. Laisha noticed an increase in her customers over a period of five consecutive weeks. Based on the pattern shown in the graph, make a conjecture about the number of customers Laisha will have in the 8th week. 10 y 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 x Week 5. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 5 is also divisible by 10. 6. Identify the hypothesis and conclusion of this conditional statement. Write the converse, inverse and contrapositive of the conditional. If two lines do not intersect at right angles, then the two lines are not perpendicular. 7. Another name for an if-then statement is a. Every conditional has two parts, what are they? 8. Write this statement as a conditional in if-then form: All rectangles have four sides. 9. Make a statement that is a counterexample for the following conditional? If you live in Illinois, then you live in Springfield.
10. What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. 11. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 4, then x 2 = 16. 12. What is the converse of the following true conditional? The inverse? The contrapositive? If two lines are parallel, they do not intersect. 13. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample. If an angle is a acute angle, its measure is less than 90. If an angle measure is less than 90, the angle is a acute angle. 14. Write the two conditional statements that make up the following biconditional. I drink coffee if (and only if) it is breakfast time. 15. One way to show that a statement is NOT a good definition is to find a. 16. Provide a counterexample to the following faulty definition? A square is a figure with four sides. 17. Draw a conclusion from the two given statements. If two angles are congruent, then they have equal measures. and are congruent. 18. Draw a conclusion from the two given statements. If you exercise regularly, then you have a healthy body. If you have a healthy body, then you have more energy. 19. Draw a conclusion from the two given statements. If two lines intersect and form right angles, then the lines are perpendicular. If two lines are perpendicular, then they intersect and form 90 angles.
20. What is the value of x? Identify the missing justifications.,, and. P R Q S x + 7 + x + 3 = 100 2x + 10 = 100 2x = 90 x = 45 a. b. Substitution Property c. Simplify d. e. Division Property of Equality 21. bisects = 6x. = 4x + 24. Find 22. Transitive Property of Congruence: Fill in the Blank. If. 23. Substitution Property of Equality: Fill in the Blank. If, then. 24. Name the Property of Congruence that justifies the statement: If. 25. Name the Property of Congruence that justifies this statement: If. 26. Complete the two-column proof. Given:
27. What is the value of x? (3x 19)º 149º 28. Find 4 1 3 2 29. Find the values of x and y. 4y 7x + 7 112 30.Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample. If x = 4, then x 2 = 16.
31.Complete the paragraph proof. Given: are supplementary, and are supplementary. By the definition of supplementary angles, _ (a) and _ (b). Then by _ (c). Subtract from each side. You get _ (d), or _ (e). 32. What are the converse, inverse, and contrapositive of the following true conditional? If a figure is a square, then it is a parallelogram. 33. Complete the two-column proof. Given: 34. Write the two conditional statements that form the given biconditional. Three points are collinear if and only if they are coplanar.