Geometry Summer Review Packet

Transcription

1 Point Pleasant Boro High School Mathematics Department Geometry Summer Review Packet * Welcome to Geometry! This summer review assignment is designed for ALL students enrolled in Geometry for the school year to refresh your Geometry skills and prepare for a successful year! π The packet is to be completed by the first day of school. π It will be collected and graded based upon completion and effort. π To receive full credit on the summer work, every problem must be attempted even if the final answer was not obtained. π Because these are not new concepts, topics in this packet will be reviewed at a rapid pace during the beginning of the school year. π All of the material in the math packet are math skills that you should had learned in your previous math classes. π A formal assessment will be given based on information reviewed in this packet during the first few weeks of school in September. π You will be required to take this assessment even if you are absent for the in-class review sessions. π When necessary, use the formulas provided in this packet and online sites to help refresh your memory! π You MUST show all work on an additional sheet of paper in order to receive credit! π Only answers are allowed to be written on this packet (all work must be shown on additional sheets of paper and remember to label your work. Have fun with the problems! =)

2 For help on all topics in this packet, go to: tinyurl.com/marronemath and click on the Summer Packet Playlist! 10 most important mathematical concepts/skills that students should know and be able to do before entering Geometry Students entering a Geometry class are expected to know and be able to demonstrate competency with the mathematical concepts and skills listed below. These concepts and skills serve as the foundation for what will be taught in Geometry. Equations: Solve and graph two-step linear equations and inequalities, and equations and inequalities with variables on both sides. Graphing: Accurately plot ordered pairs, and graph linear equations and inequalities on a coordinate plane. Integers: Demonstrate fluency in computing with integers (add, subtract, multiply, divide) and simplifying algebraic expressions involving integers. Measurement: Correctly use a ruler (standard and metric) to obtain measurements to a specific degree of accuracy, and use a protractor to measure angles. Order of operations: Understand and use the order of operations to simplify expressions and perform calculations (with rational numbers, decimals, integers, integer exponents and radicals). Properties: Understand the distributive property and how to use it to simplify expressions, solve equations and multiply binomials. Ratio: Understand the meaning and use of ratio, rates and proportions. Slope: Explain the meaning of slope as a constant rate of change, and understand how to find the slope of a line. Square roots: Understand the meaning of a square root, and use them in calculations. Translating information: Translate information from problem situations or statements into equations and inequalities.

3 Topic 1: Geometry Essential Definitions Topic 2: Angles and Angle Pairs 3. For the following problems, use the diagram on the right:

4 4. A and B are complementary angles. If the measure of A is 42, what is the measure of B? 5. J and K form a linear pair. If the measure of J is 113, what is the measure of K? 6. E and F are vertical angles. If m E = 17x + 1 and m F = 20x 14, find m F. 7. Topic 3: Segment Addition and Angle Addition Postulates 8-9. For the following problems, use the figure on the right: 8. If RS = 10 and ST = 9, what is RT? 9. If RS = 8y + 4, ST = 4y + 8, and RT = 15y 9, what is the length of RT? Find the value of PT for each of the following:

5 Use the picture on the right for the following problems: Topic 4: Distance Formula Find the distance between each set of coordinate points 17. A(5, 8) and B(-1, -4) 18. C(-5, 9) and D(-2, 7) 19. E(-3, -7) and F(3, -5) 20. G(2, -6) and H(-8, 5)

6 Write the equation of the line shown Topic 5: Graphing in a Coordinate Plane Use the slopes to determine if PQ and RS are parallel, perpendicular, or neither Find the area of the following figures. Topic 6: Area and Volume

7 33. A triangle with an area of 45.5cm 2 has a base that measures 14cm. Find the height of the triangle. 34. A parallelogram with an area of in 2 has a height that measures 7.5 in. Find the length of the parallelogram Find the volume and surface area of the given figures below:

8 Topic 7: Pythagorean Theorem Find the value of x. Round your answers to the nearest tenth For the following, determine whether the triangle is acute, right, obtuse or not a triangle , 7, ,22, , 15, , 12, 13