8. prove that triangle is a scalene triangle, right triangle, and/or an isosceles triangle. (evaluation)
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1 Subject: Geometry Unit: Analytic Geometry Grade: 10 Students will: 1. compare parallel and perpendicular slopes. (analysis) 2. find the slope of a line given two points. (application) 3. find the length of a line segment given two endpoints using the Pythagorean Theorem. (application) 4. find the length of a line segment given two endpoints on a coordinate plane using the distance formula. (synthesis) 5. classify triangles according to their sides. (analysis) 6. classify triangles according to their angles. (analysis) 7. learn the 6 steps for coordinate proofs. (knowledge) 8. prove that triangle is a scalene triangle, right triangle, and/or an isosceles triangle. (evaluation) 9. investigate, justify, and apply theorems about the sum of the measures of the angles of a triangle. (evaluation) 10. justify that points are vertices of a particular triangle (geometry proof). (evaluation) Common Core Standards addressed: Use coordinates to prove simple geometric theorems algebraically 4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, rad 3 ) lies on the circle centered at the origin and containing the point (0,2). 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
2 Prove geometric theorems 10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point
3 Name: Date: 2/17/13 Geometry R Period: Miss. O Malley Analytic Geometry Test Time: You will have two class periods to complete this test (approximately 80 minutes). Format: On this test you will find 44 questions, for a total of 100 points. It will consist of two parts: Part I (Completed on Day 1): 40 questions 10 binary choice questions each worth 1 point for a total of 10 points 10 fill in the blank questions each worth 1 points for a total of 10 points 10 matching questions each worth 1 point for a total of 10 points 10 multiple choice questions each worth 1 point for a total of 10 points Part II (Completed on Day 2): 4 questions 4 essay/proof type questions, each worth 15 points for a total of 60 points Directions: Write all answers directly on the test. Show all work and do not leave any questions blank. You will not be able to go back to Part I of the test on Day 2. If you are unsure of an answer, take your best educated guess. ****Do not stress about this test! Do your best and you will be fine! If you have any questions, raise your hand and I will answer them /False Directions: (Numbers 1-6; 1 point each; 6 points total) For each statement below, circle true if the statement is true or false if the statement is false. False 1. Two lines with the same slopes are parallel lines. False 2. Perpendicular lines form a right angle. False 3. The slope of a horizontal line is undefined. False 4. An isosceles right triangle has two equal sides and a right angle. False 5. The lines and are perpendicular. False 6. The slope of the line is.
4 Matching Directions: (Items 7-12; 1 point each; total 6 points) For each definition in column A, choose the term from column B. Write the letter of the chosen term in the blank beside the title. You will have two terms left over. Column A-Definition 7. a triangle in which all three sides have different lengths 8. an angle whose degree measure is greater than 0 and less than a triangle with three congruent sides 10. an angle whose degree measure is greater than 90 and less than a triangle with two sides that are the same length 12. angles that have the same measure Column B- Term (A) acute (B) scalene (C) isosceles (D) equilateral (E) right (F) obtuse (G) congruent (H) straight
5 Fill in the blank directions: (Items 13-18; 1 point each; total 6 points) Write the correct answer on the line below each question. 13. What is the Pythagorean Theorem? 14. What is the distance formula? 15. What is the slope formula? 16. What is the point/slope formula for the equation of a line? 17. What is the distance of line AB when A is and B is 18. What is the slope of the points and?
6 Multiple choice directions: (Items 19-24; 1 point each; total 6 points) Write the capital letter of the correct answer to each item on the blank to the left of each number. 19. When the coordinates of X are (2,-3) and the coordinates of Y are (2,7), what does XY equal? 4 B. -4 C. 10 D What is the slope of the line whose equation is? B. 2 C. -2 D The endpoints of are and. What are the coordinates of the midpoint of? (-2,3) B. (2,-3) C. (-2,-3) D. (2,3) 22. The slope of line y is. What is the slope of a line perpendicular to line y? B. C. D. 23. The coordinates of two points are (0,6) and (3,0). What is the equation of the line through these points? B. C. D. 24. What is the equation of the line that passes through the point (0,-9) and has a slope of 6? B. C. D.
7 Essays Directions: (Items 25-28; 10 points each; 40 points total) On the essay paper provided, answer each essay. Make sure you answer all aspects of each question (spelling and punctuation do not count). 25. Explain how you would justify that points B(2,2), C(-1,-1), D(2,-1) is an isosceles right triangle (HINT: 6 step proof) 26. In geometry, when completing coordinate proofs, there are different properties of quadrilaterals you need to know in order to justify the proof. List the properties of the following polygons: parallelogram, rhombus, isosceles trapezoid 27. Explain three different ways that geometric figures can be used to represent real world situations? 28. Think about what we learned this past unit about analytic geometry. Next, write a note to a student who wasn t in class yesterday. In your note, explain the important aspects of analytic geometry.
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Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during