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Geometry 1: Intro to Geometry Introduction to Geometry Name ______________________________________ Period _______________ Date _________________ G-CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line. 3. In the figure MO bisects LMN , mLMO (9 x 14) , and mNMO ( x 74) . Solve for x and find mLMN 1. Use the figure below. Assume that lines that look parallel are parallel. a) Name a pair of parallel lines b) Name a pair of perpendicular lines 4. In the figure ST bisects UX , If UW 8 x 4 , and WX 2 x 20 . Solve for x and find UX 2. Use the diagram below to answer the following questions. S W U B C A X T D O E 5. If x 100, then what are the possible values of y? 2a) Name a linear pair x° y° 2b) Name two complementary angles 2c) Name two supplementary angles 2d) Give at least two pairs of adjacent angles Geometry: Intro to Geometry Review (May 30, 2014) PUHSD Curriculum Team 6. If x < 35, then what are the possible values of y? 9. Part A: Draw a diagram that satisfies these three conditions: i. AEB CED ii. BEC is adjacent to CED iii. AEB BEC y° x° 7. Using the diagram below, find x and explain how you would tell a fellow student to solve it. Part B: If , find . Justify your answers. Solve: _________________________________ __________________________________ (4x)° x° 20° __________________________________ __________________________________ Explain___________________________ __________________________________ __________________________________ 8. Write down as many facts as are observable from the figure below. (Need at least 3) G-CO.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. 10. Construct the perpendicular bisector of RP R P Geometry 1: Intro to Geometry Review (May 29, 2014) PUHSD Geometry Curriculum Team 11. Draw acute angle ABC and then construct its bisector. Label all your points. 12. Draw a right angle and then construct its bisector. Label all your points. What are the measures of the two smaller angles? 13. Construct a copy of the angle. 14. Use a straightedge and compass to construct a segment that satisfies SN = 2(SU) and that all of the points are collinear. Explain why U is the midpoint of SN? S U Explain: _________________________________ __________________________________ __________________________________ __________________________________ Geometry 1: Intro to Geometry Review (May 29, 2014) PUHSD Geometry Curriculum Team G-CO.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. 15. Draw a diagram that fits the following criteria: Draw two lines and a transversal such that 1 and 2 are corresponding angles, 2 and 3 are vertical angles, and 3 and 4 are corresponding angles. What type of angle pair is 1 and 4? G-GPE.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, √3) lies on the circle centered at the origin and containing the point (0, 2). 17. Given the following coordinates A (-1,6) and B (3,-2). Find the midpoint and length of AB. 16. Which lines, if any, must be parallel based on the given diagram and information. Give the justification for each conclusion. Given: 13 12 a 1 2 G-GPE.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). 9 10 3 4 11 12 18. Given the equation 6y - 2x = 18, what would the slope of the line be that is: b 5 6 7 8 c 13 14 15 16 a) Perpendicular d b) Parallel Geometry 1: Intro to Geometry Review (May 29, 2014) PUHSD Geometry Curriculum Team