Mathematics Department Summer Course Work. Plane Geometry

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1 Bergenfield High School Bergenfield, New Jerse Mathematics Department Summer Course Work in preparation for Plane Geometr Completion of this summer work is required on the first da for the school ear. Student Name:

2 Bergenfield Public Schools Mathematics Department 80 South Prospect Avenue Bergenfield, New Jerse (0) June 08 Dear Parents and Guardians: We are ecited again to present summer activities that the math teachers of Bergenfield High School have created. Enclosed are math activities designed to help our son or daughter practice the skills which the have alread learned and are critical to success in this course. As ou ma be aware, studies have shown that students who do not practice or review during the summer months the material the have alread mastered lose some of that master. Unfortunatel, this then requires the net teacher to spend valuable teaching time reviewing. While certainl not the final answer, this packet of activities is designed to help our son or daughter retain his or her math skills and knowledge. Like ou, we want our child to enjo a wonderful summer. That is wh we have designed activities so that 0 to 30 minutes of work per week should be all that is required. We urge ou to encourage our child to take this task seriousl and complete it successfull. Together we can make a difference in our child s future. Now is the time to build on the foundation to help our child succeed on future standardized eams such as the PARCC, and even more importantl, the SAT. These activities will reinforce skills that were taught in previous courses. This assignment is voluntar and will not be graded but is recommended to ensure success in this course. Calculators are NOT to be used to complete this project ecept where noted. Please read all directions carefull. We wish ou a wonderful and safer summer. Sincerel, Jim Fasano Carmen Archetto Principal Director of Mathematics K - 3

3 Solve each equation. Then check our solution. Solving Linear Equations. 8 6 d r 8. 3k 7k 4. v s 9 7s ( 3) 7

4 . ABC is an equilateral triangle. B Find. Find the length of side AB A C. The perimeter of rectangle PQRS is 40 cm. Q Find. Find the area of PQRS. + 6 P - 8 R S 3. The two line segments below have the same length. Find the length of each segment The perimeter of square JKLM is 64 units. Find the length of each side. J K a + 7 M L

5 Pthagorean Theorem c a b c Eample: Step : Set-up Equation c Step : Multipl 44 c Step 3: Add 69 c Step 4: Take square root of each side. 69 c Step : Simplif square roots. 3 c b c a b 6

6 GRAPHING Instruction: Plot each point on the graph below. Remember, coordinate pairs are labeled (, ). Label each point on the graph with the letter given. 9. A(3, 4) 0. B(4, 0). C(-4, ). D(-3, -) 3. E(0, 7) Eample: F(-6, ) + F F - + Determine the coordinates for each point below: 4. Eample. (, 3) 7

7 Slope and Midpoint slope midpo int, Before using the slope or midpoint formula, ou must label our,,, and. Eample: For the points (0, ) and (, ), label our,,, and so that ou can use them in our slope or midpoint formula. Step : Label one point as point and the other as point. Point Point (0, ) and (, ) Step : Label the - and -coordinates of point as and, respectivel. Then, label the - and -coordinates of point as and. Point Point (0, ) and (, ) Eample : Use the slope formula to find the slope of the line between (0, ) and (, 3). Step : Label,,, and. Point : (0, ) Point : (, 3) 8

8 Step : Plug values into the slope formula. slope 3 slope 0 Step 3: Simplif. slope. Find the slope of the line between (, 3) and (, ). 6. Find the slope of the line between (, 3) and (9, 7). Eample : Use the midpoint formula to find the midpoint of the segment below. Step : Find the coordinates of the endpoints (-4, ) and (4, 3) Step : Label,,, and. (-4, ) and (4, 3) Step 3: Plug into midpoint formula. and simplif. midpo int, 9

9 midpo int ( 4) 4 3, 0 4 midpo int, = (0, ) 7. Find the midpoint of the segment with endpoints (0, 0) and (4, ). 8. Find the midpoint of the segment with endpoints (-3, -) and (3, 3). Factoring Methods: GCF, Sum/Product, Grouping