OHS GEOMETRY SUMMER ASSIGNMENT

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1 OHS GEOMETRY SUMMER ASSIGNMENT Name: Date Started: Complete each of the following exercises in this formative assessment. To receive full credit for this assignment, you must show your work in this packet, and complete ALL of the problems in the packet. You may use a calculator to assist you, but this cannot serve as a replacement for showing work. This assignment is due, on the first day of school (at the start of your class). This packet consists of Common Core State Standards review material, from previous grades. There are two parts of this assignment. The first part is an Algebra Review. The second part is a Geometry Review/Preview that consists of a NOTES section for each category to help you complete the EXERCISES section. Failure to complete this packet may put you at a disadvantage. For assistance in completing individual problems, you should refer to your notes from previous classes, use on-line resources, or work with your peers and family members. If you find you are having trouble with an item, skip it, and come back to it later, but persevere in trying to solve the problem. There will be time, with your teacher, in class, devoted to answering any questions regarding this summer packet. You will be assessed on this material in class, so make sure you understand how to do all of these items in this packet. You will need a TI-84 plus or TI-84 plus silver graphing calculator for Geometry Class. If you have questions regarding this assignment, please contact Mr. Porco, Mathematics Department Chair at Oxford High School, at porcos@oxfordpublicschools.org Mrs. Hall, Mathematics Teacher, at hallc@oxfordpublicschools.org, or Mrs. Caiazzo, Mathematics Teacher, at caiazzok@oxfordpublicschools.org.

2 PART 1 ALGEBRA REVIEW SECTIONS Operations with Rational Numbers: Add, Subtract, Multiply or Divide. 1. ( 2)( 3)( 4) ( 0.5) Simplifying and Evaluating Expressions Evaluate each expression if x 3and y x 2 6. y2 1 5 x x + y 8. x(y 2 + 1) Simplify each expression (4 6)

3 Distributive Property and Simplifying Expressions Simplify each of the following algebraic expressions ( x + 7) 14. 3r(5r + 2) 4(2r 2 r + 3) 15. 3(5x 2y + 6z) Solving Linear Equations Solve for x x = x + 9x 3 + x = x+9 2 = 3x 4 Slope of Lines and Writing Linear Equations 19. What is the slope of a line through the points ( 2, 2) and (2, 6)? 20. What is the equation in slope-intercept form of the line that is parallel and perpendicular to the line y = 2x 3 and passes through the point ( 1, 1)?

4 Dimensional Analysis Converting Units of Measure Convert each of the following values as indicated. An example and explanation have been provided. Example: A football field measures 100 yards in length. How many inches long is the football field? 100 yards 1 3 feet 12 inches 3600 inches = 3600 inches 1 yard 1 foot 1 Use dimensional analysis (label-cancelling method) demonstrated in the above example to convert each of the following values miles = yards days = minutes kilometers = meters Radical Expressions You must know the following facts regarding numbers that are perfect squares. We will focus on only the positive values. 1 2 = 1 therefore 2 2 = 4 therefore = 9 therefore = 16 therefore = 25 therefore = 36 therefore = 49 therefore = 64 therefore = 81 therefore = 100 therefore = = = Solve for the unknown b 2 = c 2 =

5 PART 2 GEOMETRY REVIEW/PREVIEW SECTIONS POINTS, LINES AND PLANES NOTES Term Diagram How to Label: Point Line Named with one italicized capital letter: D Named by one italicized lowercase letter: m or any two points on the line with a line symbol drawn over them: AB or BA Line Segment Named by two points (called endpoints) with a segment drawn over them: AB or BA Ray Named by two points on the ray. The endpoint should always be named first with a ray symbol drawn over them: AB Plane Named by one italicized capital letter: W or by any three non-collinear (not on the same line) points: ANF, AFB, BAF, BFA, FAB, or FBA When you name a ray, an arrowhead is not drawn over the beginning point. When you name a plane with three points, choose no more than two collinear points (points on the same line). An arrow indicates the direction of a path that extends without end. A plane is represented by a parallelogram. However, the plane actually has no edges. It is flat and extends forever in all directions. Coplanar points: points that lie in the same plane. Points D, E, and F are coplanar points. Collinear points: points that lie on the same line. Points P, Q and R are collinear.

6 EXERCISES Identify each figure below as a point, segment, ray, line, or plane, and name each. 29. Identify 30. Identify 31. Identify Name Name Name 32. Identify 33. Identify 34. Identify Name Name Name Identify the planes below using 3 vertices. 35. front 36. right-side Use the figure below. Name the intersection of each pair of planes or lines. 37. planes ABP and BCD 38. RQ and RO

7 MEASURING SEGMENTS NOTES The Segment Addition Postulate allows you to use known segment lengths to find unknown segment lengths. If three points, A, B, and C, are on the same line, and point B is between points A and C, then the distance AC is the sum of the distances AB and BC. Problem: If QS = 7 and QR = 3, what is RS? AB + BC = AC QR + RS = QS Segment Addition Postulate 3 + RS = 7 Substitute RS = 4 Solve The midpoint of a line segment divides the segment into two segments that are equal in length. If you know the distance between the midpoint and an endpoint of a segment, you can find the length of the segment. If you know the length of a segment, you can find the distance between its endpoint and midpoint. X is the midpoint of WY. XW = XY, so XW and XY are congruent (equal in measure). PROBLEM C is the midpoint of BE. If BC = t + 1, and CE = 15 t, what is BE? BC = CE t + 1 = 15 t t = 7 Definition of midpoint Substitute Solve BC = t + 1 = (7)+1 = 8 BC = 8 BE = 2(BC) = 2(8) = 16 BE = 16

8 EXERCISES Use the figure below. 39. If PN = 29 cm and MN = 13 cm, then PM = 40. If MN = 82 and PN = 105, then PM = 41. If PM = 3x + 2 and MN = 2x + 4, and PN = 31, find x. 42. M is the midpoint of PN. If PM = x + 23, and MN = 2x + 8, what is x?

9 MEASURING ANGLES NOTES The vertex of an angle is the common endpoint of the rays that form the angle. An angle may be named by its vertex. It may also be named by a number or by a point on each ray and the vertex (in the middle). Correct Names: Z, XZY, YZX, or 1. Incorrect Names: ZYX, XYZ, YXZ, or ZXY. Angles are measured in degrees, and the measure of an angle is used to classify it. The Angle Addition Postulate allows you to use a known angle measure to find an unknown angle measure. If point B is in the interior of AXC, the sum of m AXB and m BXC is equal to m AXC. m AXB + m BXC = m AXC PROBLEM If m LYN = 125, what are m LYM and m MYN? m LYM + m MYN = m LYN Angle Addition Postulate (4p + 7) + (2p 2) = 125 Substitute p= 20 Solve m LYM = 4p + 7=4(20) + 7=87 m LYM = 87 m MYN = 2p 2= 2(20) 2= 38 m MYN = 38

10 EXERCISES Use the figure at the right. 43. What are three other names for S?,, 44. What type of angle is S? 45. Name the vertex of each angle. a. LGH b. MBX Classify the following angles as acute, right, obtuse, or straight 46. m LGH = m SLI = m L = 179 Use the figure at the right. Find the measure of each angle. 49. ADB= 50. FDE = 51. ADC = 52. BDE= 53. The combined measure of the angles is 90. <1 = 3x + 7 and <2 = 2x + 3, find x.

11 EXPLORING ANGLE PAIRS NOTES Adjacent Angles and Vertical Angles Adjacent means next to. Angles are adjacent if they lie next to each other. In other words, the angles have the same vertex and they share a side without overlapping. Adjacent Angles Overlapping Angles Vertical means related to the vertex. So, angles are vertical if they share a vertex, but not just any vertex. They share a vertex formed by the intersection of two straight lines. Vertical angles are always congruent. Vertical Angles Non-Vertical Angles Supplementary Angles and Complementary Angles Two angles that form a line are supplementary angles. Another term for these angles is a linear pair. However, any two angles with measures that sum to 180 are also considered supplementary angles. In both figures below, m 1 = 120 and m 2 = 60, so 1 and 2 are supplementary. Two angles that form a right angle are complementary angles. However, any two angles with measures that sum to 90 are also considered complementary angles. In both figures below, m 1 = 60 and m 2 = 30, so 1 and 2 are complementary.

12 EXERCISES 54. Use the diagram below. a. Name an angle that overlaps ABE. b. Name an angle adjacent to ABD. c. Name an angle that is supplementary to ABE. What is the measure of this angle? d. Name an angle that is complementary to EBF. What is the measure of this angle? 55. Use the diagram below. a. Name the vertical angle to DOE. b. Name the vertical angle to AOE.

13 PERIMETER, CIRCUMFERENCE, AND AREA NOTES Polygons: are closed figures, made up of line segments that meet only at their end points and are on one plane. The perimeter of a polygon is the sum of the lengths of its sides. So, the perimeter is the distance around its outside. The area of a polygon is the number of square units it encloses. For figures such as squares, rectangles, triangles and circles, you can use formulas for perimeter (or circumference C for circles) and area. Formulas for Perimeter, Area and Circumference:

14 EXERCISES 56. Fill in the missing information for each square in the table below. Side Perimeter, P = 4s Area, A = s 2 3 cm 4 3 cm = 12 cm. (3 cm) 2 = 9 cm 2 4 cm 5 cm 10 cm 57. Fill in the missing information for each rectangle in the table below. Dimensions Perimeter, P = 2(b + h) Area, A = bh 1 ft 9 ft 2(1 ft + 9 ft) = 20 ft 1 ft 9 ft = 9 ft 2 2 ft 8 ft 3 ft 7 ft 4 ft 6 ft 58. Find the area of a triangle with a base of 8 and a height of Fill in the missing information for each circle in the table below. Radius Diameter, D = 2r Circumference, C = 2πr Area, A = πr 2 2 in. 2 2 = 4 in. 2π 2 in. = 4π in. π (2 in. ) 2 = 4π in. 2 3 in. 5 in. 8 in. 10 in. 60. Find the area of the composite figure below.

OHS GEOMETRY SUMMER ASSIGNMENT

OHS GEOMETRY SUMMER ASSIGNMENT Name: Date Started: Complete each of the following exercises in this formative assessment. To receive full credit for this assignment, you must show your work in this packet,