Geometry EOC Review. ALIGNED TO GEOMETRY CROSSWALK P.E.s. Compiled By Stanwood Camano School District Teachers

Size: px

Start display at page:

Download "Geometry EOC Review. ALIGNED TO GEOMETRY CROSSWALK P.E.s. Compiled By Stanwood Camano School District Teachers"

Alexia Peters
5 years ago
Views:

1 Geometry EOC Review ALIGNED TO GEOMETRY CROSSWALK P.E.s Compiled By Stanwood Camano School District Teachers March, 2011

2 G.1 CORE CONTENT: Logical Arguments & Proofs G.I.C. Use deductive reasoning to prove that a valid geometric statement is true. 1. Determine if the conjecture is valid by the Law of Syllogism. Given: If an animal is a mammal, then it has hair. If an animal is a dog, then it is a mammal. Conjecture: If an animal is a dog, then it has hair. Istheconjecturevalid? Whyorwhynot? 2. Draw a conclusion from the given information. If two angles form a linear pair, then they are adjacent. If two angles are adjacent, then they share a common side. 1 and 2 form a linear pair. Conclusion: G.1.D. Write the converse, inverse, and contrapositive of a valid proposition and determine Statetheconverse: their validity. 3. If m and n are odd integers, then the sum of m and n is an even integer. State the converse and determine whether it is valid. Isitvalid?Whyorwhynot?

3 4. If an animal is a cat, then it has four paws. Write the converse, inverse, and contrapositive and determine whether the statement is valid. Converse: Isitvalid? Inverse: Isitvalid? Contrapositive: Isitvalid? G.1.E. Identify errors or gaps in a mathematical argument and develop counterexamples to refute invalid statements about geometric relationships. 5 Which of the following conjectures is false? o A. o B. o C. o D. If X is odd, then X + 1 is even. The sum of two odd integers is even. The difference of two even numbers is positive. If X is positive, then X is negative. 6. A student conjectures that if X is a prime number, then X + 1 is not prime. Which of the following is a counterexample? o A. X = 11 o B. X = 6 o C. X = 3 o D. X = 2

4 G.1.F. Explain the role of definitions, undefined terms, postulates (axioms) and theorems. 7. There are two definitions of trapezoid that can be found in books or on the web. A trapezoid is either a quadrilateral with exactly one pair of parallel sides OR a quadrilateral with at least one pair of parallel sides. Write a theorem that is true when applied to one definition but not the other, and explain your answer in the box below. 8. Determinewhichofthefollowingstatementsisanundefinedterm. o A. Alinesegmentisapartofalineconsistingoftwopointsandallpoints between. o B.Arayisapartofalinethatstartsatanendpointandextendsforeverin onedirection. o C.Alineisastraightpaththathasnothicknessandextendsforever. o D.Oppositeraysaretworaysthathaveacommonendpointandformsa line. 9.Apostulateisastatementthat: o A. o B. o C. o D. canbeprovenusingdefinitions. isaformaltheoremaboutageometricfigure. isacceptedastruewithoutproof. definesageometricfigureusingalgebra.

5 G.3 CORE CONTENT: 2 & 3 DIMENSIONAL FIGURES G.3.A. Know and apply basic postulates and theorems about triangles 10. Triangle JKE is an obtuse isosceles triangle with m E = 10 and KE > JK. What is the measure of J? o A. 170 o B. 160 o C. 85 o D. 10 G.3.B Determine and prove triangle congruence. 11.

6 G.3.C. Use properties of special right triangles to solve problems. 12. The pitch of a symmetrical roof on a house 40 feet wide is 30º. What is the length of the rafter, r, exactly and approximately? exactly approximately G.3.D Know and apply the Pythagorean Theorem and its converse. 13.A juice box is 6 cm by 8 cm by 12 cm. A straw is inserted into a hole in the center of the top of the box. The straw must stick out 2 cm so you can drink from it. If the straw must be long enough to touch each bottom corner of the box, what is the minimum length the straw must be? (Assume the diameter of the straw is 0 for the mathematical model.) Minimum length of straw

7 G.3.E Solve problems involving trigonometric ratios of sine, cosine and tangent. 14. Three circular disks are placed next to each other as shown. The disks have radii of 4 cm, 5 cm, and 6 cm. The centers of the disks form YXZ. Find m YXZ to the nearest degree. Measure of XYZ to the nearest degree. G.3.F Know, prove, and apply basic theorems about parallelograms. 15. In parallelogram PQRS the measurers of angle P and angle R are each 146. What is the measure of angle Q? o A. 146 o B. 112 o C. 68 o D. 34

8 16. The diagram shows the parallelogram-shaped component that attaches a car s rearview mirror to the car. In parallelogram RSTU, UR= 25, RX = 16, and m STU = Find ST, XT, and m RST. o A. ST = 16, m RST = 42.4, XT = 25 o B. ST = 25, m RST = 47.8, XT = 16 o C. ST = 25, m RST = 137.6, XT = 16 o D. ST = 5, m RST = 137.6, XT = 4 G.3.G Know and apply theorems about properties of quadrilaterals and other polygons. 17. Find RS. o A. RS = 18 o B. RS = 24 o C. RS = 20 o D. RS = 16

9 G.4 CORE CONTENT: GEOMETRY IN THE COORDINATE PLANE G.4.B Determine the coordinates of a point that it described geometrically. 18. What are the coordinates of point Z? (, ) G.4.C Apply properties of triangles and quadrilaterals in the coordinate plane. 19. Find the circumcenter of ABC with vertices A(-2, 4), B(-2, -2), and C(4, -2). o A. (1,1) o B. (0, 0) o C. (, ) o D (-2, -2)

10 G.6 CORE CONTENT: ADDITIONAL KEY CONTENT G.6.E Use different degrees of precision in measurement, explain reason for using a certain degree and apply estimation strategies. 20. The contractor from Thompson s Building Company was measuring a large picture window in order to begin cutting a rectangle in the side of the building to accommodate this window. Which measurement should the builder use to allow for the least amount of error in his measuring? o A. o B. o C. o D. millimeters centimeters decimeter meter Explain you re your reasoning in the space below. G.6.F Solve problems involving measurement conversions and analyze solutions in terms of reasonableness. 21. Jenny has a jewelry box that has a volume of 29 cubic inches. 1 inch = 2.54 centimeters. Determine the volume of the jewelry box to the nearest cubic centimeter. Write your answer on the line. Whatisthevolumeofthejewelryboxtothenearestcubiccentimeter?

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST. Name: Date:

NORTH THURSTON PUBLIC SCHOOLS END OF COURSE GEOMETRY PRACTICE TEST Name: Date: Day 1 1. Determine the value of x if ΔABC is equilateral. B 7.5x 6x + 3 A Write your answer on the line. 10x 5 C What is the