Geometry Summer Packet

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Geometry Summer Packet Name ALLEN PARK HIGH SCHOOL Summer Assessment Geometry Summer Packet For Students Entering Geometry Summer 04 This summer packet is intended to be completed by the FIRST DAY of

1 Geometry Summer Packet Name ALLEN PARK HIGH SCHOOL Summer Assessment Geometry Summer Packet For Students Entering Geometry Summer 04 This summer packet is intended to be completed by the FIRST DAY of school. This packet will be graded and count as the first grade of the marking period. You should be working on the packet for the class you are taking NEXT YEAR. Feel free to me if you have any questions regarding your packet by ing me at: We encourage you to check your answers and re-work any problems that were incorrect. We expect you to spend at least hour each week on your summer math packet. This packet is not designed for one intense 0 hour session the day before school starts so begin now! This summer math packet will be worth 50 points and will be the first recorded grade of the marking period. Bring your questions and concerns regarding any problems you may have had difficulty with to your class on the first day of school, September 4 th. Start off the year with a great start by completing the packet to the best of your ability. APHS/MATH Page

2 Geometry Summer Packet Summer 04 Show all work for all problems, regardless of their level of difficulty. Answers will be in the form of positive, negative, whole numbers, fractions and decimals. Leave answers in fraction form unless the question contains decimals. Order of Operations Remember PEMDAS (Please Excuse My Dear Aunt Sally) You must perform the order of operations in a specific order. P: Parentheses (Grouping symbols: parentheses( ), brackets [ ], braces { }, and fraction bars ). E: Exponents, such as. MD: Multiply OR Divide (compute whatever appears st moving from left to right) AS: Add OR Subtract (compute whatever appears st moving from left to right) Example : Add Multiply Exp. subtract Add Divide st Example : 94()( 0) = split into parts 4()( 0) x multiply add evaluate 7 7 and 4 0 and and 5 Find the value of each expression APHS/MATH Page

3 Geometry Summer Packet Summer (4)(8) ()() 4. 5 ()(5) ()(5) 4. 4()(6) Simplifying Expressions Simplifying expressions involves collecting like terms. 8 xand x are like terms 5 xand 6y are not like terms When simplifying expressions you must follow the order of operations. Example : Simplify the expression. 9x 5 x 7.5 9x x x x x.5 Change the order like terms like terms 4x 7 x 4 4x 7 x 4 4x 7 x 4 Example : Simplify the expression. Distribute the 8x 4 x 4 8x x 4 4 like terms like terms change the order 8x x4 4 9x 8 Simplify each expression. 5. k 0k 6. 8x x 7. 5( 8 a) 6a APHS/MATH Page

4 Geometry Summer Packet Summer a 5a 9. (7x 9) 0 0. ( x9) (5x 6). 0(n 4) 6( n ). 8.k 5.6k a a 6 6 Solving Equations Remember the general rule: What you do to one side, you must do to the other. If you add a number to one side of the equation, you must add the same number to the other. This rule holds true for adding, subtracting, multiplying, and dividing numbers or variables to each side of an equation. Example : Solve. 5x x6 5x x6 Add x to both sides x x 7x 6 Subtract from both sides 7x 4 7x 4 Divide both sides by x Example : Solve. 4 x 9 4 Cross Multiply x 9 6 Subtract x Example : Solve. x 5 x 5 Add 5 to both sides 5 5 x 6 Multiply both sides by x 6 which is the reciprocal of 4 x 4 x 7 x x 4 Divide by Solve each equation x n APHS/MATH Page 4

5 Geometry Summer Packet Summer 04 n x x 0. 7 x 4. r n 6n. 4y 6 4. m 6 m 5. 6( 7 x) b b x b 6b 6( b ) 9. y 40. 8( x7) 4(5x 7) x 7 5 x 0 APHS/MATH Page 5

6 Geometry Summer Packet Summer y ( y ) x x ( 5y ) ( y5) 8 Distance Between Two Points on the Coordinate Plane Example : Find the distance between the pair of points (5, ),(,7). You must pick one point to be point and the other to be point. Point has an x and a y coordinate. Point will have xand y and point will have xand y. For this example (5, ),(, 7). Plug these numbers into the distance formula as follows. x y x y d ( x x ) ( y y ) = ( 5) (7 ( )) = ( 8) (9) combine combine 7+ "square" "square" = 64 8 both are always positive - now add = 45 =.04 square round to root decimal places The distance between two points can also be interpreted as the length of the segment between the two endpoints. Find the distance between each pair of points. Distance Formula: d ( x x ) ( y y ) 45. (,4),(, 5) 46. (,8),(8,0) 47. (,0),( 7,) 48. ( 8,4),(, 7) 49. (, 4),(,) 50. ( 4,4),( 4,4) APHS/MATH Page 6

7 Geometry Summer Packet Summer 04 Midpoint Between Two Points on the Coordinate Plane Example : Find the midpoint of the line segment with the given endpoints (5, ),(,7). You must pick one point to be point and the other to be point. Point has an x and a y coordinate. Point will have xand y and point will have xand y. For this example (5, ),(, 7). Plug these numbers into the midpoint formula as follows. mp x y x y combine 5 combine 7 x x y y 5 ( ) ( ) 7 5..,, =, =,.5 simplify The midpoint is the point that is half way between the two given endpoints. x x y y Find the midpoint of the line segment with the given endpoints. Midpoint Formula: mp.., 5. ( 5, 5),(4,5) 5. (,),(7,9) 5. (, 4),( 5,0) 54. (,9),(,5) 55. ( 4, 9),( 7, 9) 56. (4,0),( 6,4) Slope of a Line on the Coordinate Plane The Slope of a line represents its steepness. A large slope such as 7 or -6 is a steep line, while a small slope such as ½ or ¼ are lines with very little steepness (they are almost horizontal lines) Example : Find the slope of the line through the two given points ( 4,6),(, ). You must pick one point to be point and the other to be point. Point has an x and a y coordinate. Point will have xand y and point will have xand y. For this example ( 4,6),(, ). Plug these numbers into the slope formula as follows. m combine 6 y y ( ) 6 9 ( 4) 6 = = x x combine 4 simplify x y x y APHS/MATH Page 7

8 Geometry Summer Packet Summer 04 y y Find the slope of the line through each pair of points. Slope Formula: m x x 57. (,8),(0, 7) 58. (6,),(8,) 59. (4, 6),( 9, 5) 60. ( 7,6),( 7,9) 6. (7,5),( 0,) 6. (, 7),( 8, ) Area Area represents the total number of squares that are required to cover the interior of a flat (plane) figure. Each polygon has its own formula that can be used to calculate the area. Use the formulas below to calculate the area of the given figure. Formulas: Rectangle/Parallelogram: A bh Triangle: A bh Circle: A r Trapezoid: A h ( b ) b b = base of the figure h = the height of the figure r = radius of a circle d = diameter of a circle =.4 Find the area of each figure. Round to the nearest hundredth when necessary APHS/MATH Page 8

9 Geometry Summer Packet Summer Circle with a radius of inches. 76. Circle with a diameter of 8 km. 77. APHS/MATH Page 9

10 Geometry Summer Packet Summer 04 Perimeter and Circumference Perimeter represents the distance around a figure. You can simply add up all of the sides of the figure. Circumference is the distance around a circle. You will use one of the two given formulas below. Formulas: Perimeter add up all of the sides Circumference: C r or C d r = radius d = diameter Find the perimeter or circumference for each figure. Round to the nearest hundredth when necessary APHS/MATH Page 0

11 Geometry Summer Packet Summer 04 Applying Geometric Terminology Below you will find multiple definitions that you will see at the beginning of the school year in Geometry. Read each definition and observe all of the information in and around the diagram. Angle and Angle are VERTICAL ANGLES Vertical Angles are Equal 4 Angle 5 and Angle 6 form a LINEAR PAIR Linear Pairs Add up to Angle 7 and Angle 8 are COMPLIMENTARY ANGLES Complimentary Angles Add up to 90. Angle and Angle 4 are VERTICAL ANGLES Vertical Angles are Equal Angle 5 and Angle 6 are also SUPPLEMENTARY ANGLES Supplementary Angles also Add up to A Ray BA and Ray BC are PERPENDICULAR Perpendicular rays, lines, and segments form a 90 angle. The angles in a triangle always Add up to 80. A 9 perpendicular lines gives 4 90 angles B C B C Using the definitions above, identify the type of angle relationships of the numbered angles below A 9 B 0 C APHS/MATH Page

12 Geometry Summer Packet Summer Find the measure of angle J. 94. Find the measure of angle D. J E 0 H F G D Use the definitions from the previous page to first write an equation for the angle relationship, then find the value of x A x - B C x+7 4x + 77 x + 40 x + 8 5x x+0 x+60 6x+80 APHS/MATH Page

PCTI Geometry. Summer Packet

PCTI Geometry. Summer Packet PCTI Geometry Summer Packet 2017 1 This packet has been designed to help you review various mathematical topics that will be necessary for your success in Geometry. INSTRUCTIONS: Do all problems without