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Honors Geometry Unit 1 Exam Review Review your Homework Quizzes, Exit Slips and Embedded Assessments, then study homework problems as needed. Know your vocabulary and how is applies to problems like 20 & 26 on page 50. Know how to write the converse & inverse of a conditional and determine validity. Know how to write a two-column proof. Know how to calculate and apply slope, distance, midpoint. Be able to find the equation of a line that is perpendicular or parallel to another given line. Understand and use the theorems and postulates we used with parallel lines and transversals. Learning Targets 1-1-1 1-1-2 1-2-1 1-2-2 2-1-1 2-2-1 2-2-2 3-1-2 3-2-1 3-2-2 3-3-1 3-3-2 4-1-1 4-1-2 4-2-1 4-2-2 5-1-2 5-2-2 6-1-1 6-1-2 6-2-1 6-2-2 7-1-1 7-1-2* 7-2-2 8-1-1* 8-1-2 8-2-1 8-2-2 Identify, describe, and name points, lines, line segments, rays and planes using correct notation. Identify and name angles. Describe angles and angle pairs. Identify and name parts of a circle. Make conjectures by applying inductive reasoning. Use deductive reasoning to prove that a conjecture is true. Develop geometric and algebraic arguments based on deductive reasoning. Use properties to complete algebraic two-column proofs. Identify the hypothesis and conclusion of a conditional statement. Give counterexamples for false conditional statements. Write and determine the truth value of the converse, inverse, and contrapositive of a conditional statement. Write and interpret biconditional statements. Apply the Segment Addition Postulate to find lengths of segments. Use the definition of midpoint to find lengths of segments. Apply the Angle Addition Postulate to find angle measures. Use the definition of angle bisector to find angle measures. Use the Distance Formula to find the distance between two points on the coordinate plane. Use the Midpoint Formula to find the coordinates of the midpoint of a segment on the coordinate plane. Use definitions, properties, and theorems to justify a statement. Write two-column proofs to prove theorems about lines and angles. Complete two-column proofs to prove theorems about segments. Complete two-column proofs to prove theorems about angles. Make conjectures about the angles formed by a pair of parallel lines and a transversal. Prove theorems about the angles formed by a pair of parallel lines and a transversal.. Determine whether lines are parallel using theorems. Make conjectures about the slopes of parallel and perpendicular lines. Use slope to determine whether lines are parallel or perpendicular. Write the equation of a line that is parallel to a given line. Write the equation of a line that is perpendicular to a given line. Vocab to Know 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. angle adjacent angles acute angle axiomatic system bi-conditional statement bisector (angle & segment) alternate interior angles chord complementary angles congruent coplanar, collinear conditional statement (hypothesis and conclusion) conjecture concentric contrapositive converse corresponding angles counterexample diameter deductive reasoning inductive reasoning inverse line linear pair 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. midpoint obtuse angle straight angle parallel lines perpendicular lines same-side interior angles supplementary angles plane point postulate proof theorem transversal truth value two-column proof radius ray right angle segment undefined terms vertical angles segment or angle addition postulate Vertical angles theorem Alternate exterior angles Same side exterior angles Not every type of problem on the exam is represented below, however these problems will allow you to refresh your memory on some concepts that you will see on the exam. It is in your best interest to use your class notes, textbook examples and homework problems to be fully prepared for the exam. 1) Complete a two-column proof: ⃗⃗⃗⃗⃗ bisects EPG Given: 𝑷𝑭 Prove: EPF = 26 o 2) Write each of the following in if-then form. Write the converse of each statement and discuss the validity of each converse. Rectangles have four sides Three points on the same line are collinear 3) Write the equation of a line parallel to the given line and through the given point. 𝑦= 1 𝑥 + 3, 2 (6,3) 4) 𝑎 ∥ 𝑏. Find x. Explain your reasoning. 5) Name the angle or angles described by each of the following: a) supplementary to NQK b) vertical to PQM c) congruent to NQJ d) adjacent and congruent to JQM e) complimentary to KQP e) forms a linear pair with PQM 6) A map of a city and suburbs shows an airport located at A(25, 11). An ambulance is on a straight expressway headed from the airport to Grant Hospital at G(1, 1). a. The ambulance gets a flat tire at the midpoint M of AG . What are their coordinates? b. How far are they from the hospital? c. Write the equation of a line that is perpendicular to AG going through the point (6,7). 7) Write a two-column proof. Given: a b , c d Prove: ∢𝟏𝟔 ≅ ∢𝟐 8) Point E is between G and T, GE 2 x, ET (3x 1) and GT 14 Find the value of x. Geometry Unit 1 Review Answers Statements ⃗⃗⃗⃗⃗ 𝑃𝐹 bisects ∡𝐸𝑃𝐺 ∢𝐸𝑃𝐹 ≅ ∢𝐹𝐷𝐺 4x+2=6x-10 2=2x-10 12=2x X=6 ∢𝐸𝑃𝐹 = 4(6) + 2 ∢𝐸𝑃𝐹 = 26 Reasons Given Definition of bisects Substitution property Subtraction property of equality Addition property of equality Division property of equality Substitution property Substitution Property 1.) Conditional – If a figure is a rectangle, then it has 4 sides. Converse – If a figure has 4 sides, then it is a rectangle. The converse is false. Counterexample – Parallelogram. Conditional – If 3 points lie on the same line, then they are collinear. Converse – If 3 points are collinear, then they are on the same lie. The converse if true by the definition of collinear. 1 2 2.) 𝑦 = 𝑥 3.) X=54, the angles are congruent by the alternate exterior angles theorem. OR Students could use corresponding angles and vertical angles to explain why the angles are congruent. 4.) Sample Answers A. ∢𝑁𝐽𝑄 𝑜𝑟 ∡𝐾𝑄𝑃 B. ∢𝐿𝑄𝑁 C. ∢𝐾𝑄𝑃 D. ∢𝐾𝑄𝑀 𝑜𝑟 ∢𝐿𝑄𝐽 E. ∢𝑃𝑄𝑀 F. ∢𝑀𝑄𝑁 𝑜𝑟 ∢𝐿𝑄𝑃 6.) M (13,6) and d=13 units 7.) Sample Answer Statements 8.) x=3 Reasons a b, c d given ∠16 ≅ ∠10 Corresponding angles postulate ∠10 ≅ ∠2 Alternate Interior angles theorem ∠16 ≅ ∠2 Transitive property