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1 FAIR LAWN PUBLIC SCHOOLS RONALD J. MEZZADRI District Supervisor Mathematics, Business & Career Education Fair Lawn High School Berdan Avenue Fair Lawn, New Jersey (01) x11 Fax (01) June, 014 Dear Parents, Your child has completed Algebra 1 and will be entering Geometry when school resumes in September. The foundation for their next step into mathematics was carefully laid out in Algebra 1 and will be expanded upon in Geometry. In order for your child to have a successful transition into Geometry it is important that every student review and practice the key concepts that were taught in Algebra 1. A packet has been provided to give your child the opportunity to accomplish this task. The packet is posted on the school website and by accessing the following link: The practice problems must be completed to the best of their ability prior to the first day of the school year. Time will be given to review solutions in class and then an assessment will be given on the material. Mastery of the fundamental concepts outlined in this packet is essential to your child s success in Geometry. Have a safe and happy summer. We look forward to a successful opening of the new school year. Sincerely, Ron Mezzadri Supervisor of Mathematics The Leaders of Tomorrow Attend Fair Lawn Schools Today

2 Geometry Summer Assignment Information Welcome to Geometry! This summer review assignment is designed to refresh your Algebra 1/Prealgebra skills. It includes information that was taught in algebra 1 and will be used daily in geometry. Due Date: This packet must be completed by the second day of school, September 4th th 014. Grading: We will review this material during the first few days of school and will then be tested on the material covered in this packet. The assessment will take place on September 16 th, 014. During the summer you should try all of the problems. If you are having difficulty, you should look at your notes from previous mathematics courses and at the websites below If you have difficulty with these topics you must see your Geometry teacher during the first week of school for extra help. Page 1

3 1. Name the following components using the figure given below: A D E B C F a.) a point b.) a segment c.) a line d.) a ray e.) an angle f.) a pair of vertical angles. The Find the value of A x m ABD D m DBC ( x + 1) B (x + 1) C 3. If,, and, find the value of. Then find the value of and. D E F Page

4 4. and are complementary. ( ) and ( ). Find the value of and the measures of both angles. 5. Find the value of x and the measure of. P (7x + ) ( x + ) L M N 6. Classify the following triangles by side length (scalene, isosceles, or equilateral) and angle measure (acute, right, or obtuse). a. b. c Using the Pythagorean theorem, a b c, find the missing side of each of the following triangles. Leave your answer in simplest radical form. a. b. 1 1 Page 3

5 8. Find the missing angle measure in each of the following triangles. The sum of the interior angles of a triangle is 180 degrees. a. b. c ) Students placed a coordinate grid over a star map and used constellations to practice transformations. The constellation triangle has 3 stars, located at points A (-6, 4), B (-4, 6), and C (-, 3). a. Plot points A, B and C. b. A new image ΔA B C is formed by translating ΔABC 8 units to the right. What are the coordinates of the new image? Plot this image. c. Plot and label the vertices of ΔA B C, the reflection of ΔA B C over the x-axis. d. On the same grid, plot and label the vertices of ΔA B C, the rotation of ΔABC 90 degrees counterclockwise about the origin. Page 4

6 10) Graph each of the following equations. A. y3(1 x) B. y y x 1 5 y x x C. x6y 1 D. y1 ( x ) y y x x E. y F. x 3 y y x x Page 5

7 11) Write an equation in slope-intercept, y=mx+b, form with the given information. A. slope = 3 4 y-intercept = - B. Through (0, ) and (1, -3) C. parallel to y=x+1 goes through (5,4) D. perpindicular to y=-4x+10 goes through (1,) 1) Write an equation in point-slope, y y1 m( x x1), form with the given information. A. slope = 3 through (4, -) B. Through (5, 4) and (-4, 3) C. parallel to y=-7x- goes through (3,-11) D. perpindicular to y= x-3 3 goes through (-,4) Page 6

8 13) Given the square below. Answers should be written as fractions in simplest form. 1 1 Midpoint Formula x x, y M y Distance Formula d ( y y ) ( x x ) 1 1 A. State the coordinates of each point. B. Find and plot the midpoints of segments AB, BC, CD, AD. C. Find the distance of the diagonal AC. Leave answer as simplest radical form. Page 7

9 Notes: There are four special angle pairs that we are going to learn about today; Alternate Interior Angles, Alternate Exterior Angles, Same side Interior Angles, and Same side exterior angles. These relationships only work if line L is parallel to line M L M Alternate Interior Angles: angles on opposite sides of the transversal (not adjacent) and between the given lines. These angles are congruent. Example: < 1 and <, < 3 and < 4 Alternate Exterior Angles: angles on opposite sides of the transversal (not adjacent) and beyond the given lines. These angles are congruent. Example: < 5 and < 8, < 6 and < 7 Same Side Interior Angles: angles on the same side of the transversal and between the given lines. These angles are supplementary. Example: < 1 and < 4, < 3 and < Same Side Exterior Angles: angles on the same side of the transversal and beyond the given lines. These angles are supplementary. Example: < 6 and < 8, < 5 and < 7 Page 8

10 14) Refer to the diagram to the right. Given that line L is parallel to line M, list two angle pairs of each indicated type. A) Alternate interior angles L B) Alternate exterior angles C) Same-side interior angles M D) Same-side exterior angles E) Corresponding angles 15) Given that m 30, find the missing angle measures. m1 m m3 m4 m5 m6 m7 m L M Page 9

11 16) Using the diagram to the right, where line L is parallel to line M, please answer the following: L M A) Given that m (30x 30) and m6 (5x 0), set up an equation to solve for x B) Using your equation from part a, solve for x. C) Find the missing angle measures. m1 ; m5 m ; m6 m3 ; m7 m4 ; m8 Page 10

12 Notes: Polygons are a very important topic in geometry. With regards to polygons, you must be able to name polygons, state the type of polygon, identify the edges, vertices, diagonals, the sum of interior and exterior diagonals, and finding the measure of an interior angle and an exterior angle. A regular polygon is defined a polygon whose sides are all congruent and all angles are congruent. POLYGONS REGULAR POLYGONS sum of interior angles 180 n degrees in one interior 180 n n sum of ext. s 360 diagonals in a polygon n n 3 one ext. 360 n 17) Find the missing angle measures. A) B) Page 11

13 18) Determine the area and perimeter of ABC. Show all work! Area of a Triangle Formula: A 1 bh Area = Perimeter = 19) Determine the area and perimeter of ABC. Show all work! Area of a Triangle Formula: A 1 bh Area = Perimeter = Page 1

14 0) Determine the area and perimeter of the parallelogram below. Show all work! Area of a parallelogram formula: A b h Area = Perimeter = 1) Determine the area and perimeter of the parallelogram below. Show all work! Area of a parallelogram formula: A b h Area = Perimeter = Page 13

15 ) Determine the area and perimeter of the trapezoid below. Show all work! 1 A b b h Area of a trapezoid formula: 1 Area = Perimeter = 3) The area of a trapezoid is 60 height? cm. The bases have lengths of 8 cm and 1 cm. What is the 4) Determine the area and perimeter of the trapezoid below. Show all work! Area and Circumference of a circle formulas: A r C r Area = Circumference= Page 14

16 5) The area of a circle is 48 cm. Determine the radius of the circle to the nearest tenth of a centimeter. Show all work! 6) The circumference of a circle is 40 cm. Determine the radius of the circle to the nearest tenth of a centimeter. Show all work! 7) Suppose you want to choose a shape below for a container of popcorn. Which shape has the largest capacity and would hold the most popcorn? Show all work! 1 Volume of a Cone Volume of Pyramid 3 rh Volume of a Rectangular Prism Volume of a Cylinder 1 Bh, where B Area of Base 3 lwh r h Page 15