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GEOMETRY FINAL REVIEW-ch.2

GEOMETRY FINAL REVIEW-ch.2. Which term best defines the type of reasoning used below? “Abdul broke out in hives the last four times that he ate chocolate candy. Abdul concludes that he will break out in hives if he eats chocolate.” Inductive Deductive Converse Inverse. a) Inductive.

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GEOMETRY FINAL REVIEW-ch.2

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  1. GEOMETRY FINAL REVIEW-ch.2 Which term best defines the type of reasoning used below? “Abdul broke out in hives the last four times that he ate chocolate candy. Abdul concludes that he will break out in hives if he eats chocolate.” • Inductive • Deductive • Converse • Inverse a) Inductive

  2. GEOMETRY FINAL REVIEW-ch.3 LJ and GH are parallel and m< L = 40°. Find the measures of the numbered angles. m< 1 = ______ m< 2 = ______ m< 3 = ______ ANSWER: m< 1 = 100° m< 2 = 40° m< 3 = 140°

  3. GEOMETRY FINAL REVIEW-ch.3 In the figure below, m<3 + m<5 = 180°. Determine which lines are parallel. Justify your reasoning. Line r is parallel to line s. Justifications may vary. One approach to justification: converse of same side interior angles theorem

  4. GEOMETRY FINAL REVIEW-ch. 2 The given statement is a valid geometric proposition.  Statement: If a triangle has two congruent angles, then it is an isosceles triangle. a) Write the contrapositive of this statement: b) NOW, Determine if the contrapositive statement is valid. Explain your reasoning. a) If a triangle is not isosceles, then the triangle does not have two angles that are congruent. b) The contrapositive statement is valid. The triangle could be equilateral, which is also isosceles. It could also be scalene, with no congruent angles. Also, the contrapositive of a true statement is always true. If a statement is false, its contrapositive will be false also.

  5. GEOMETRY FINAL REVIEW-ch. 2 The given statement is a valid geometric proposition. Statement: If a quadrilateral is a kite, then its diagonals are perpendicular. Which of the following is the inverse statement? a) If a quadrilateral has diagonals that are perpendicular, then it is a kite. b) If a quadrilateral is not a kite, then its diagonals are not perpendicular. c) If a quadrilateral has diagonals that are not perpendicular, then it is not a kite. d) If a quadrilateral is a kite, then its diagonals are not perpendicular B

  6. GEOMETRY FINAL REVIEW-ch. 5 Which is the correct construction of a perpendicular bisector of AB? C

  7. GEOMETRY FINAL REVIEW-ch. 3 Which is the correct construction of a line segment parallel to AB passing through point C? C

  8. GEOMETRY FINAL REVIEW-ch.1 Complete the following statements. a) The ceiling and floor of your kitchen are examples of __________planes. b) A wall and the floor of your kitchen are examples of _____________planes. Word choices: Coplanar Parallel Skew Perpendicular • Parallel • Perpendicular

  9. GEOMETRY FINAL REVIEW-ch.1  Complete the following statement: Two lines that do not lie in the same plane are called ________________ lines.  a) Coplanar b) Parallel c) Skew d) Perpendicular C

  10. GEOMETRY FINAL REVIEW-ch. 5 In ΔABC, point I is the incenter. m < BAI = x + 4 m < IAC = 2x – 6 Find the value of x. x=10

  11. GEOMETRY FINAL REVIEW-ch. 5 ΔLPT is an obtuse scalene triangle. If P is the obtuse angle in the triangle, which of the following is not a valid conclusion? a) m< L + m T < m <P b) m< L + m <T < 90° c) m<L + m<T = 90° d) m < L + m < T + m < P = 180° C

  12. GEOMETRY FINAL REVIEW-ch. 5 Which triangle has an altitude that is also a median?

  13. GEOMETRY FINAL REVIEW In the diagram below, <E ≅ <D and AE ≅ CD. Prove AB ≅ CB using mathematical language and concepts. One approach to the justification: <E ≅ <D and AE ≅ CD Given < ABE ≅<CBD Vertical angles are congruent. ABE ≅ CDB AAS AB ≅ CB Corresponding Pts of Congr. s are Congruent (CPCTC)

  14. GEOMETRY FINAL REVIEW-ch. 1 In the triangle below, how long is AC? • 6 • 9.1 • 10 • 14.1  B(7,5) A(-2,-3) C(7,-2) B

  15. GEOMETRY FINAL REVIEW-ch. 8 The hypotenuse of a 45°-45°-90° triangle measures 10 inches. What is the area of the triangle? A) 25 in2 B) in2 C)50in2 in2 A

  16. GEOMETRY FINAL REVIEW-ch. 8 Triangle ABC is equilateral, with side lengths of 10 inches. What is the length, in inches, of AD? A)V B) C) 5 D) 5 D

  17. GEOMETRY FINAL REVIEW-ch. 8 What is the m< R, to the nearest degree, in the figure below? A) 60° B) 36° C)30° D) 27° A

  18. GEOMETRY FINAL REVIEW-ch. 8 At a distance of 20 m from a building, a person who is 3 m tall looks up at an angle of 25° to see the top of the building. How tall is the building to the nearest meter?(HINT: Draw a picture) A)8 m B) 9 m C) 12 m D)18 m B

  19. GEOMETRY FINAL REVIEW-ch. 8 Find the length of the hypotenuse, to the nearest tenth of a centimeter, of a right triangle if one angle measures 70° and the adjacent leg measures 8 cm. (HINT: Draw a picture) 23.4 cm

  20. GEOMETRY FINAL REVIEW-ch. 8 Find the value of a in the figure below, to the nearest whole number. A) 10 B) 11 C) 14 D) 16 B

  21. GEOMETRY FINAL REVIEW-ch. 6 In the parallelogram below, WV = 5x + 2 and YV = -x + 20. Find WY. A) 17 B) 20 C) 34 D) 50 C

  22. GEOMETRY FINAL REVIEW-ch.6 In the parallelogram below, m < ABC = 70°. Find m < ACD. m<ACD=65⁰

  23. GEOMETRY FINAL REVIEW-ch.6 X=7 The perimeter of the figure below is 48. Find the value of x.

  24. GEOMETRY FINAL REVIEW-ch. 6 • Complete the proof of the following statement: • If the diagonals of a quadrilateral bisect each • other, then the quadrilateral is a parallelogram. • Given: AC and BD bisect each other. • Prove: ABCD is a parallelogram. 1) AC and BD bisect each other. 1) Given 2) 2) Definition of Bisect • BECDEA 3) _____________________ BEA DEC • BECDEA 4) ________________ BEA DEC • 1 2 5)__________________ 3 4 6) 6) Alternate Interior Angles Theorem 7)_______________ 7) Definition of Parallelogram Vertical angles are . SAS CPCTC (Corr. Parts or congruent triangles are Converse of ABCD is a parallelogram.

  25. GEOMETRY FINAL REVIEW-ch. 11 A trapezoidal prism has ____ total faces. A) 4 B) 5 C) 6 D) 7 A)4

  26. GEOMETRY FINAL REVIEW-ch. 11 If a plane intersects a cube, the intersection of the plane and cube cannot be a(an) ___________. a) Triangle b) Square c) Rectangle d) Octagon d) Octagon

  27. GEOMETRY FINAL REVIEW-ch.1 AC starts at point A (1,4), and ends at point C (7, 13). What are the coordinates of the midpoint of AC? (4, 8.5)

  28. GEOMETRY FINAL REVIEW-ch.1 Given points A (0, -3), B (5, 3), Q (-3, -1), which of the following points is a location of P so that PQ is parallel to AB? a) (0,3) b) (12,5) c) (-7,11) d) (2,5) d

  29. GEOMETRY FINAL REVIEW-ch.12 Suppose triangle ABC has vertices A (-5,-2), B (-6,-2), and C (-6,-6). If triangle ABC is rotated 90° counterclockwise about the origin, what are the coordinates of the vertices of triangle A’B’C’? (HINT: use your reasoning skills) • A’ (2,-5), B’ (2, -6), C’ (6, -6) • A’ (-5,2), B’ (-6,2), C’ (-6,6) c) A’ (5,-2), B’ (6,-2), C’ (-6,-6) d) A’ (2,-5), B’ (-2,-6), C’ (-6,-6) a

  30. GEOMETRY FINAL REVIEW-ch.12 How many lines of symmetry does the polygon shown have? a) 0 b) 1 c) 2 d) 3 1

  31. GEOMETRY FINAL REVIEW-ch. 10 Find the area of the sector in circle P if PA = 10 cm and measure of arc APB = 36°. a) 10πcm2 b) 20π cm2 c) 36π cm2 d) 72π cm2 a

  32. GEOMETRY FINAL REVIEW-ch. 10 Find the area of the shaded region. Area of square = 256 cm2 (16*16) Area of circle = 64π cm2 (82) Area shaded region = 256 - 64π cm2 or approx. 55.04 cm2

  33. GEOMETRY FINAL REVIEW-ch. 10 In circle P, find the area of the shaded region. Use an approximate value of 3.14 for π. a) 3.14 square units b) 4.56 square units c) 6.28 square units d) 9.62 square units b

  34. GEOMETRY FINAL REVIEW-ch. 10 In circle Q, find the measure of arc ADB. a) 42° b) 138° c) 222° d) 318 c

  35. GEOMETRY FINAL REVIEW-ch. 10 In circle P, find the length of arc AB if PA = 10 and m<APB = 36°. a) 2 π b) 0.556 π c) 10 π d) 12 π a

  36. GEOMETRY FINAL REVIEW-ch.10 What is the length of the apothem of a regular hexagon with side length 8 m ? What is the area of the hexagon? Apothem: m Area:

  37. GEOMETRY FINAL REVIEW-ch. 10 The area of a sector of a circle is 54 π cm2. If the central angle is 60°, what is the radius of the circle? Radius = 18 cm

  38. GEOMETRY FINAL REVIEW-ch. 11 Two cylinders have the same height. Their radii are 6 cm and 3 cm. What is the ratio of the volume of the cylinder with radius 6 cm to the volume of the cylinder with radius 3 cm? 4:1

  39. GEOMETRY FINAL REVIEW-ch.11 If the volume of a cone is 96 π cm 3 and the base of the cone has a radius of 6 cm, find the height of the cone. • 2.55 cm • 8 cm • 16 cm • 48 cm b

  40. GEOMETRY FINAL REVIEW-ch. 11 Donna wants to put a ceramic castle whose volume is 350 cm3 and a plastic scuba diver whose volume is 250 cm3 in her aquarium as decoration. Her aquarium measures 40 cm X 30 cm X 30 cm high. The water is 2 cm from the top before she begins to decorate. How much will the water rise when she puts the castle and the diver in? • 0.5 cm • 1 cm • 2 cm • 6 cm a

  41. GEOMETRY FINAL REVIEW-ch. 11 Cube A has side lengths that are two times as long as the sides of cube B. How many times larger is cube A’s volume than that of cube B? • 2 • 4 • 6 • 8 d

  42. GEOMETRY FINAL REVIEW-ch. 2 & ch. 6 Consider these statements: Every square is a rhombus. Quadrilateral ABCD is not a rhombus. Which of these conclusions can be made using both statements? • ABCD is not a parallelogram. • ABCD is a rectangle. • ABCD is not a square. • ABCDis a trapezoid c

  43. GEOMETRY FINAL REVIEW-ch. 2 Melanie, Nikki, and Donny are three students in a geometry class. Melanie is younger than Nikki, and Donny is older than Nikki. Which of these must be true? • Donny is the youngest of the three students. • Melanie is the youngest of the three students. • Nikki is the oldest of the three students. • Melanie is the oldest of the three students. b

  44. GEOMETRY FINAL REVIEW-previous course If the pattern shown below continues, how many squares will be in the next figure? • 6 • 8 • 16 • 64 b 1 8 2 16 4 32

  45. GEOMETRY FINAL REVIEW-ch. 2 The two statements below are true. All simkos are temas. All bollies are simkos. Using deductive reasoning, which of these statements must also be true? • All temas are bollies. • All simkos are bollies. • All temas are simkos. • All bollies are temas.   d

  46. GEOMETRY FINAL REVIEW-ch. 5 Given: AF ≅ FC Use the word bank below the triangle to name each special segment in ΔABC. Word Bank: Median, Angle Bisector, Perpendicular Bisector, Altitude BF: ______________ FG: _______________ BF: Median FG: Perpendicular Bisector

  47. GEOMETRY FINAL REVIEW-ch. 5 Given: ABE ≅ EBC. Use the word bank below the triangle to name each special segment in ΔABC. Word Bank: Median, Angle Bisector, Perpendicular Bisector, Altitude BD: _____________ EB: ______________ BD: Altitude EB: Angle Bisector

  48. GEOMETRY FINAL REVIEW-ch.3 and ch.4 Jennifer has created a two-column proof as a response to the following question. Evaluate her argument to determine if you support or contradict her conclusion. Given: LA ≅PS, LS ≅PA Prove: LA ll PS Statement Reason LA ≅ PS 1) Given SL ≅ AP 2) Given SA ≅AS 3) Same Segment/Reflexive ΔLAS ≅ΔPSA4) SSS ΔPSA ≅ΔLSA5) Corresponding Parts of Congruent Triangles are Congruent LA ll PS 6) Conv. Alt. Interior anglesThm Determine if Jennifer’s argument is valid. Explain your reasoning. Support your answer with evidence from the diagram or Jennifer’s proof. Jennifer’s argument is not valid. On step 5 of her proof, she states that ΔPSA ≅ ΔLSA. This would indicate that LSll PA and not LA ll PS. Jennifer should have stated that ΔLAS ≅ ΔPSA.

  49. GEOMETRY FINAL REVIEW-ch. 11 B

  50. GEOMETRY FINAL REVIEW-ch. 1 and ch. 4 5. <ABD 6. SAS

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