Geometry Semester 1 REVIEW
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1 Name: Class: Date: ID: A Geometry Semester 1 REVIEW 1. The figure below is a rectangular shipping box. Name two different planes that contain BC. 2. Find BC. 3. The endpoints of GH are GÊ Ë Á 6, 9 ˆ and H Ê ËÁ 8, 7 ˆ. Find the coordinates of the midpoint M. 4. Find the area of FGH with coordinates FÊ Ë Á 4, 6 ˆ,G Ê Ë Á1,3 ˆ, and H Ê ËÁ 2, 6 ˆ. 1
2 ID: A 5. Find m BDC. 6. A ramp that is used to load a truck makes supplementary angles with the ground. The ramp has an incline ( 1) of 25. What is the measure of 2? 7. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the converse. Then decide whether it is true or false. 8. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the inverse. Then decide whether it is true or false. 9. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the contrapositive. Then decide whether it is true or false. 2
3 ID: A If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements. 10. If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it has four right angles. Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain your reasoning. 11. All mammals are warm-blooded. Snakes are not warm-blooded. Your pet snake is not a mammal. State the law of logic that is illustrated. 12. If you get an A on your math test, then you can choose where to go to dinner. If you can choose where to dinner, then you can go to your favorite restaurant. If you get an A on your math test, then you can go to your favorite restaurant. 13. Determine which statements about the diagram you cannot conclude. a. Line n and BD intersect at point D. c. Points A, B, and C are collinear. b. Line m is perpendicular to plane S. d. Line m intersects plane S at point C. Name the property that the statement illustrates. 14. If MN XY and XY RS, then MN RS 3
4 ID: A 15. CD CD 16. EFG EFG Identify the numbered statement or reason in the two-column proof. Given ABC is a right angle. Prove x = 8 STATEMENTS REASONS 1. ABC is a right angle. 1. Given 2. m ABC = Angle Addition Postulate 4. (6x + 5) + (5x 3) = Substitution Property of Equality 5. 11x + 2 = Simplify Subtraction Property of Equality 7. x = What is Reason 2? a. Given c. Definition of complementary angles b. Definition of a right angle d. Angle Addition Postulate 4
5 ID: A 18. Find the values of x and y. 19. Each yard line of a football field is parallel to the yard line immediately to the right of it. Explain why the left 10-yard line is parallel to the right 10-yard line. 20. Find the value of x that makes a Ä b if c ll d. 5
6 ID: A 21. Find the distance from point P to RQ. a. 58 units c. about 7.6 units b. about 7.1 units d. 10 units 22. Determine which of the lines are parallel and which of the lines are perpendicular. 23. Write an equation of the line passing through the point (4, 6) that is parallel to the line y = 8x 11. 6
7 ID: A 24. An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule Ê Ë Á x, y ˆ Ê ËÁ x + 9, y 9 ˆ. Later, the client decides that they would prefer the water fountain s location moved from this new position 5 units left and 2 units down. Find the composition as a single transformation. 25. In the diagram, name the vector and select its component form. 26. A student wants to apply a series of transformations to ABC. The student first applies a translation to the triangle, but then must decide whether to apply a reflection. Select all transformations used by the student to create the image AʺBʺC ʺ. a. reflection in x-axis c. reflection in y-axis b. Ê Ë Á x, y ˆ Ê Ë Áx 4, y + 3 ˆ d. Ê Ë Áx, yˆ Ê ËÁ x + 3, y + 4 ˆ 7
8 ID: A 27. Graph AB with endpoints A(3, 4) and B(3, 1) and its image after a reflection in the line y = x. 28. Graph the polygon and its image after a rotation of 270 counterclockwise about the origin. 29. In the diagram, the figure is reflected in line a. The image is then reflected in line b. Describe a single transformation that maps F to F ʺ. 30. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 8
9 ID: A 31. Find m KMN. 32. Classify PQR by its sides. Then determine whether it is a right triangle. a. isoceles ; not right c. isoceles ; right b. scalene ; right d. scalene ; not right 9
10 ID: A 33. Find the value of x. 34. Find the value of x. 10
11 ID: A 35. In the diagram of the roller coaster track below, can you use the Hypotenuse-Leg Congruence Theorem to prove that RSQ TQS? 36. Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use. 11
12 ID: A 37. A road crew uses the triangles shown in the diagram to measure the width of a sink hole across a highway from a safe distance away. How wide is the sink hole? 38. In the diagram, AD bisects BAC. Find BD. 12
13 ID: A 39. Find AC. 40. A company builds trusses to support structures. In the truss shown below, the support GH is the midsegment of ABC. Find the value of x. 13
14 ID: A 41. You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need? 42. List the sides of ABC from shortest to longest. 43. A triangle has one side that measures 3 feet and another side that measures 30 inches. Which are possible side lengths of the third side? a. 1 in. c. 72 in. b. 42 in. d. 30 in. 14
15 ID: A 44. For an art project you need to create a design that involves only triangles. One of the triangles you cut out is shown below. List the angles of ABC in order from smallest to largest. 45. Complete the statement AD CD with <, >, or =. 15
16 ID: A Geometry Semester 1 REVIEW Answer Section 1. ANS: plane CAD, plane BFG 2. ANS: ANS: Ê ËÁ 1, 8 ˆ 4. ANS: 27 square units 5. ANS: ANS: ANS: If an animal is a golden retriever, then it is a dog; true 8. ANS: If an animal is not a dog, then it is not a golden retriever; true 9. ANS: If an animal is not a golden retriever, then it is not a dog; false 10. ANS: If a figure is a square, then it has four right angles. 11. ANS: deductive reasoning; Facts are used. 12. ANS: Law of Syllogism 13. ANS: B, C 14. ANS: Transitive Property of Segment Congruence 15. ANS: Reflexive Property of Segment Congruence 16. ANS: Reflexive Property of Angle Congruence 17. ANS: B 18. ANS: x = 3, y = ANS: By The Transitive Property of Parallel Lines, the left 10-yard line is parallel to the right 10-yard line. 20. ANS: ANS: B 22. ANS: a Ä b c a c b 1
17 ID: A 23. ANS: y = 8x ANS: Ê Ë Á x, y ˆ Ê ËÁ x + 4, y 11 ˆ 25. ANS: CB, 2, ANS: A, D 27. ANS: 28. ANS: 29. ANS: 40 rotation about point J 30. ANS: 9 4 ; enlargement 31. ANS: ANS: C 33. ANS: 4 2
18 ID: A 34. ANS: ANS: yes 36. ANS: yes; AAS Congruence Theorem 37. ANS: 18 ft 38. ANS: BD = ANS: AC = ANS: 10 ft 41. ANS: 216 ft 42. ANS: AB, AC, CB 43. ANS: B, D 44. ANS: B, C, A 45. ANS: = 3
19 Geometry Semester 1 REVIEW [Answer Strip] ID: A 21. B 32. C 26. A, D 13. B, C 43. B, D 17. B
20 Name: Class: Date: ID: B Geometry Semester 1 REVIEW Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain your reasoning. 1. All mammals are warm-blooded. Snakes are not warm-blooded. Your pet snake is not a mammal. 2. A triangle has one side that measures 3 feet and another side that measures 30 inches. Which are possible side lengths of the third side? a. 30 in. c. 72 in. b. 42 in. d. 1 in. 3. You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need? 4. Graph AB with endpoints A(3, 4) and B(3, 1) and its image after a reflection in the line y = x. 5. Graph the polygon and its image after a rotation of 270 counterclockwise about the origin. 1
21 ID: B 6. For an art project you need to create a design that involves only triangles. One of the triangles you cut out is shown below. List the angles of ABC in order from smallest to largest. Name the property that the statement illustrates. 7. EFG EFG 8. If MN XY and XY RS, then MN RS 9. CD CD 10. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the converse. Then decide whether it is true or false. 2
22 ID: B 11. Each yard line of a football field is parallel to the yard line immediately to the right of it. Explain why the left 10-yard line is parallel to the right 10-yard line. 12. The figure below is a rectangular shipping box. Name two different planes that contain BC. 13. Find m BDC. 3
23 ID: B 14. In the diagram, AD bisects BAC. Find BD. 15. Determine which of the lines are parallel and which of the lines are perpendicular. 4
24 ID: B 16. A ramp that is used to load a truck makes supplementary angles with the ground. The ramp has an incline ( 1) of 25. What is the measure of 2? 17. In the diagram, name the vector and select its component form. 5
25 ID: B 18. Find the value of x that makes a Ä b if c ll d. 19. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the contrapositive. Then decide whether it is true or false. 20. Find the value of x. 21. The endpoints of GH are GÊ Ë Á 6, 9 ˆ and H Ê ËÁ 8, 7 ˆ. Find the coordinates of the midpoint M. 6
26 ID: B 22. Classify PQR by its sides. Then determine whether it is a right triangle. a. isoceles ; not right c. isoceles ; right b. scalene ; not right d. scalene ; right 23. Complete the statement AD CD with <, >, or =. 7
27 ID: B 24. Find the value of x. 25. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 8
28 ID: B 26. A road crew uses the triangles shown in the diagram to measure the width of a sink hole across a highway from a safe distance away. How wide is the sink hole? If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements. 27. If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it has four right angles. 28. Let p be an animal is a dog and let q be an animal is a golden retriever. Write the inverse. Then decide whether it is true or false. 9
29 ID: B 29. Find m KMN. 30. Find the values of x and y. 31. Find BC. 10
30 ID: B Determine which statements about the diagram you cannot conclude. 32. a. Line m intersects plane S at point C. c. Line n and BD intersect at point D. b. Line m is perpendicular to plane S. d. Points A, B, and C are collinear. 33. A company builds trusses to support structures. In the truss shown below, the support GH is the midsegment of ABC. Find the value of x. 34. List the sides of ABC from shortest to longest. 11
31 ID: B 35. Find the distance from point P to RQ. a. about 7.1 units c. 10 units b. 58 units d. about 7.6 units 36. Find AC. State the law of logic that is illustrated. 37. If you get an A on your math test, then you can choose where to go to dinner. If you can choose where to dinner, then you can go to your favorite restaurant. If you get an A on your math test, then you can go to your favorite restaurant. 12
32 ID: B 38. Write an equation of the line passing through the point (4, 6) that is parallel to the line y = 8x Find the area of FGH with coordinates FÊ Ë Á 4, 6 ˆ,G Ê Ë Á1,3 ˆ, and H Ê ËÁ 2, 6 ˆ. 40. In the diagram, the figure is reflected in line a. The image is then reflected in line b. Describe a single transformation that maps F to F ʺ. 41. Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use. 13
33 ID: B 42. An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule Ê Ë Á x, y ˆ Ê ËÁ x + 9, y 9 ˆ. Later, the client decides that they would prefer the water fountain s location moved from this new position 5 units left and 2 units down. Find the composition as a single transformation. 43. In the diagram of the roller coaster track below, can you use the Hypotenuse-Leg Congruence Theorem to prove that RSQ TQS? 44. A student wants to apply a series of transformations to ABC. The student first applies a translation to the triangle, but then must decide whether to apply a reflection. Select all transformations used by the student to create the image AʺBʺC ʺ. a. reflection in x-axis c. Ê Ë x, y Ê ËÁ x 4, y + 3 ˆ b. reflection in y-axis d. Ê Ë x, y Ê ËÁ x + 3, y + 4 ˆ 14
34 ID: B Identify the numbered statement or reason in the two-column proof. Given ABC is a right angle. Prove x = 8 STATEMENTS REASONS 1. ABC is a right angle. 1. Given 2. m ABC = Angle Addition Postulate 4. (6x + 5) + (5x 3) = Substitution Property of Equality 5. 11x + 2 = Simplify Subtraction Property of Equality 7. x = What is Reason 2? a. Angle Addition Postulate c. Given b. Definition of complementary angles d. Definition of a right angle 15
35 ID: B Geometry Semester 1 REVIEW Answer Section 1. ANS: deductive reasoning; Facts are used. 2. ANS: A, B 3. ANS: 216 ft 4. ANS: 5. ANS: 6. ANS: B, C, A 7. ANS: Reflexive Property of Angle Congruence 8. ANS: Transitive Property of Segment Congruence 9. ANS: Reflexive Property of Segment Congruence 10. ANS: If an animal is a golden retriever, then it is a dog; true 1
36 ID: B 11. ANS: By The Transitive Property of Parallel Lines, the left 10-yard line is parallel to the right 10-yard line. 12. ANS: plane CAD, plane BFG 13. ANS: ANS: BD = ANS: a Ä b c a c b 16. ANS: ANS: CB, 2, ANS: ANS: If an animal is not a golden retriever, then it is not a dog; false 20. ANS: ANS: Ê ËÁ 1, 8 ˆ 22. ANS: C 23. ANS: = 24. ANS: ANS: 9 4 ; enlargement 26. ANS: 18 ft 27. ANS: If a figure is a square, then it has four right angles. 28. ANS: If an animal is not a dog, then it is not a golden retriever; true 29. ANS: ANS: x = 3, y = ANS: ANS: B, D 2
37 ID: B 33. ANS: 10 ft 34. ANS: AB, AC, CB 35. ANS: A 36. ANS: AC = ANS: Law of Syllogism 38. ANS: y = 8x ANS: 27 square units 40. ANS: 40 rotation about point J 41. ANS: yes; AAS Congruence Theorem 42. ANS: Ê Ë Á x, y ˆ Ê ËÁ x + 4, y 11 ˆ 43. ANS: yes 44. ANS: A, D 45. ANS: D 3
38 Geometry Semester 1 REVIEW [Answer Strip] ID: B 22. C 35. A 32. B, D A, B A, D 45. D
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