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Geometry 1: Introduction to Geometry Review 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. 1. 3. In the figure SP bisects RST , mRSP (9 x 14) , and mTSP ( x 74) . Solve for x and find mRST Use the figure at the right. Assume that lines that look parallel are parallel and lines that look perpendicular are perpendicular. a) Name a pair of parallel segments b) Name a pair of perpendicular segments 4. Given the following, find the length of TL and TO . c) Name a pair of skew segments 2. Use the diagram at the right to answer the following questions. a) Name a linear pair b) Name two complementary angles - T is the midpoint of XO - The length of XO is 10 - HL is 8 c) Name two supplementary angles d) Name two adjacent angles to ∠ORN e) Name a pair of vertical angles TL = ____________ TO = ____________ Geometry: Intro to Geometry Review PUHSD Curriculum Team 5. Using the diagram below, find x and justify each step. AEB BEC . Solve: Part A: Draw a diagram that satisfies these three conditions (4x)° x° Steps: 7. You know that AEB CED , BEC is adjacent to CED , and 20° Justification: Part B: If 𝑚∠𝐴𝐸𝐵 = 30°, find 𝑚∠𝐵𝐸𝐶, 𝑚∠𝐶𝐸𝐷 𝑎𝑛𝑑 𝑚∠𝐴𝐸𝐷. Justify your answers. _________________________________ __________________________________ __________________________________ 6. Circle all of the following statements that are definitely true about the diagram below. (There may be more than one answer.) __________________________________ 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. 8. Construct the perpendicular bisector of RP R (a) AEB DEC (b) AEC is adjacent to BED (c) AEB and BEC are complementary (d) DEC and BEC are complementary (e) EC bisects BED (f) DEA is supplementary Geometry 1: Intro to Geometry Review P PUHSD Geometry Curriculum Team 9. Given A construct its bisector. 11. Given the diagram below, Name a pair of each of the following. Alternate interior angles _________________ 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. Same side interior angles ________________ Vertical angles ________________________ Alternate exterior angles ________________ Corresponding angles __________________ 10. Given that lines a line b. Linear Pair __________________________ 12. Which lines, if any, must be parallel based on the given diagram and information. Justify your answer. Given: 13 12 a 1 2 9 10 3 4 Part A: Find the value of x. b 11 12 5 6 7 8 c Part B: Describe the relationship between these two angles. 13 14 15 16 d _____________________________________________ _____________________________________________ _____________________________________________ Geometry 1: Intro to Geometry Review PUHSD Geometry Curriculum Team G-GPE.4: Use coordinates to prove simple geometric G-GPE.5: Prove the slope criteria for parallel and 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). 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). 15. Given the equation y = - 4x + 8 13. Given X(-2, 3) and Y(3,-1). Part A: Find the midpoint. Part A: Give an example of a line parallel to the one given above. Part B: Find the distance. Part B: Give an example of a line perpendicular to the one given above. Part C: Find the slope. 16. Given the equation 6y - 2x = 18. 14. Given the following coordinates A (-1,6) and B (3,-2). Find the midpoint of AB and label it M. How would you prove that M is the midpoint? y Part A: What is the slope of this line? Part B: Write an example of an equation of a line that is perpendicular to the original line. 10 Part C: Write an example of an equation of line that is parallel to the original line. –10 10 x –10 Geometry 1: Intro to Geometry Review PUHSD Geometry Curriculum Team