Geometry Cumulative Study Guide Test 8

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Geometry Cumulative Study Guide Test 8 Numeric Response 1. A rectangular plot of land has a length of 3.5 miles and a width of 8.5 miles. What is the area, in square miles, of the plot of land? 2. A circle has a diameter of 11 inches. What is the area, in square inches, of the circle to the nearest square inch? Use 3.14 for. 3. WXYZ is a parallelogram. Find the value of x. W 2x + 9 X Name: Date: Period: 6. In the right triangle CDE, measures and the right angle is at vertex C. Find. 7. Write the biconditional of the statement and its converse. If, then. Is it true? Explain why or why not. 8. Use the Law of Syllogism to write a valid set of conditional statements for the following three statements in the form If p, then q. If q, then r. If p, then r. p: q: r: Z 4x + 5 4. The diagram shows the floor of a living room. What area, in square feet, of carpet will be needed to cover the floor? Y 9. Solve the equation below. Provide a justification for each step. 10. For,,,. For,,,. Write the congruency statement for the triangles. 11. What is the included angle of? 12. Find the value of x in the triangle below. Write your answer in simplified radical form. Problem 5. Write the inverse of the statement below. Is the statement true? Is the inverse of the statement true? 9 x 6

2 13. Compare the measures of. S 5 5 U 42 43 T 4 4 W 14. Use the given paragraph proof to write a twocolumn proof. V X 17. Rosa must design a flag that will be exactly the same size as the triangle below. The flag will contain a right angle. Rosa knows that she only needs to pick two other dimensions to make sure that the flag is congruent to the triangle. List all the pairs of dimensions Rosa could use to ensure the flag is exactly the same size and shape as the triangle. For each pair of dimensions, write which triangle congruence theorem applies. C Given: Triangle XYZ is a right triangle. is a right angle. Prove: and are complementary angles. A B Triangle XYZ is a right triangle, and is a right angle. So, by the definition of a right angle. By the Triangle Sum Theorem,. By the Subtraction Property of Equality,. So,. Therefore, and are complementary angles by the definition of complementary angles. 18. Are the lines y = x + 3 and y = 2 x parallel, perpendicular, or neither? 19. Using the diagram below, find YZ if XW = 14, ZW = 10, and XY = 2. 15. Find the centroid of with vertices at E ( 4, 1), F (2, 3), and G ( 4, 1). 16. Determine whether the triangle below is a right triangle. 13 19 20. Decide whether each set of side lengths could form a valid triangle: (6, 14, 16), (8, 13, 12), and (9, 13, 18) 14

3 Cumulative Study Guide Test 8 Geometry Answer Section NUMERIC RESPONSE 1. ANS: 29.75 REF: Lesson 22: Finding Areas of Quadrilaterals NAT: NCTM M.2b TOP: Cumulative Test 8 MSC: Geom_S03_00059 2. ANS: 95 REF: Lesson 23: Introduction to Circles NAT: NCTM M.2b TOP: Cumulative Test 8 MSC: Geom_S03_00065 3. ANS: 2 REF: Lesson 34: Properties of Parallelograms NAT: NCTM A.2b TOP: Cumulative Test 8 MSC: Geom_S04_00058 4. ANS: 386 REF: Lesson 40: Finding Perimeters and Areas of Composite Figures NAT: NCTM M.2b TOP: Cumulative Test 8 MSC: Geom_S04_00062 PROBLEM 5. ANS: true. Both the statement and it inverse are REF: Lesson 17: More Conditional Statements NAT: NCTM RP.1b TOP: Cumulative Test 8 MSC: Geom_S02_00102 6. ANS: REF: Lesson 18: Triangle Theorems NAT: NCTM G.1d TOP: Cumulative Test 8 MSC: Geom_S02_00109 7. ANS: if and only if. For the biconditional to be true, both the statement and its converse must be true. In this case, the converse, if then, is not true, so the biconditional is not true.

4 REF: Lesson 20: Interpreting Truth Tables NAT: NCTM RP.1b TOP: Cumulative Test 8 MSC: Geom_S02_00115 8. ANS: If p, then q: AND if q, then r: THEN If p, then r: REF: Lesson 21: Laws of Detachment and Syllogism NAT: NCTM RP.1c TOP: Cumulative Test 8 MSC: Geom_S03_00075 9. ANS: Given Distributive Property Addition Property of Equality Simplify Subtraction Property of Equality Simplify Division Property of Equality Simplify REF: Lesson 24: Algebraic Proofs NAT: NCTM A.2b TOP: Cumulative Test 8 MSC: Geom_S03_00083 10. ANS: REF: Lesson 25: Triangle Congruence: SSS NAT: NCTM CM.1d TOP: Cumulative Test 8 MSC: Geom_S03_00088 11. ANS: REF: Lesson 28: Triangle Congruence: SAS MSC: Geom_S03_00096 12. ANS: 3 13 REF: Lesson 29: Using the Pythagorean Theorem NAT: NCTM G.1d TOP: Cumulative Test 8 MSC: Geom_S03_00100 13. ANS: REF: Investigation 4: Inequalities in Two Triangles

5 NAT: NCTM G.1b TOP: Cumulative Test 8 MSC: Geom_S04_00069 14. ANS: Statements Reasons 1. is a right triangle. 1. Given 2. is a right angle. 2. Given 3. 3. Definition of right angle 4. 4. Triangle Sum Theorem 5. 5. Subtraction Property of Equality 6. 6. Simplify 7. 7. Substitution 8. 8. Simplify 9. and are complementary angles. 9. Definition of complementary angles REF: Lesson 31: Flowchart and Paragraph Proofs NAT: NCTM RP.1c TOP: Cumulative Test 8 MSC: Geom_S04_00071 15. ANS: ( 2, 1) REF: Lesson 32: Altitudes and Medians of Triangles MSC: Geom_S04_00072 16. ANS: The triangle is not a right triangle by the Converse of the Pythagorean Theorem. REF: Lesson 33: Converse of the Pythagorean Theorem MSC: Geom_S04_00074 17. ANS: AB and (LA); AB and (LA); AC and (HA); AB and BC (LL); AC and BC (HL); BC and (LA); BC and (LA); AC and (HA); AC and AB (HL) REF: Lesson 36: Right Triangle Congruence Theorems NAT: NCTM G.1b TOP: Cumulative Test 8 MSC: Geom_S04_00083 18. ANS: Parallel REF: Lesson 37: Writing Equations of Parallel and Perpendicular Lines NAT: NCTM A.4 TOP: Cumulative Test 8 MSC: Geom_S04_00085 19. ANS: YZ = 1 3 7 REF: Lesson 38: Perpendicular and Angle Bisectors of Triangles NAT: NCTM G.1b TOP: Cumulative Test 8 MSC: Geom_S04_00091 20. ANS:

6 yes, yes, and yes REF: Lesson 39: Inequalities in a Triangle MSC: Geom_S04_00093

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