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1. Construct the perpendicular bisector of the segments below. using smaller arcs Name ____________________ Date ________________ CC Geometry R HW #9A Constructing a Perpendicular Bisector using larger arcs L A B M 2. Construct the line perpendicular to line l through point A. Number the steps in the correct order, from 1 - 5. 3 A 5 4 2 l 1 Draw circle(arc) B: center B and circle C(center C), using two equal radii that intersect. Draw AD. Label D, the intersection of arcs B and C. Label the two points of intersection as B and C. Draw circle(arc)A: center A, intersecting l in two points. 3. Construct the perpendicular bisectors of AB, BC , and CA on the triangle below. What do you notice about the segments you have constructed? The three perpendicular bisectors intersect in the same point. They are CONCURRENT. A B C OVER 4. Two homes are built on a plot of land. Both homeowners have dogs, and are interested in putting up as much fencing as possible between their homes on the land, but in a way that keeps the fence equidistant from each home. Use your construction tools to determine where the fence should go on the plot of land. perpendicular bisector H2 of H1H2 H1 Review 2 5. In ΔABC, ≮B = ≮C. If AB = x + 8x and AC = 20. a) Label the diagram. b) Write and solve a quadratic equation for x. There will be two answers. A 2 x + 8x = 20 x2 + 8x 20 x = 10 / x = 2 B C c) If BC = 3x + 5, choose the appropriate value for x, and find the perimeter of Perimeter = 20 + 20 + 11 = 51 BC = 3x + 5 ΔABC. BC = 3(2) + 5 = 11 6. Find x, and classify the triangle by its angles. co 78o (2x+4)o 65o (2x9)o 7) Find the variables. a 83o do o bo 37oxo fo 1260 (2x + 4) + (2x 9) + x = 180 5x 5 = 180 go 5x = 185 x = 37 eo 56o 54 c = ____ 34 43 b = ____ a = ____ acute triangle 27 e = ____ 110 126 g = ____ 27 f = ____ d = ____ Aim/Hwk 9B Construction Practice Math 10X Name____________________________________ Show all construction marks. 1. Construct and label the perpendicular bisector XY of AB. B A 2. Construct and label equilateral ΔABC using segment DE as a side length. D E 60° A 3. Construct and label bisector QS of PQR P Q S R 4. Construct and label ≮ XYZ equal in measure to ≮ ABC. X A B C Y Z 0 5. Construct ≮HEF which measure 30 . angle bisector of 60O H 60°30° F E 6. Construct a line perpendicular to the given line through the given point P. Clearly and precisely list the steps needed to accomplish this construction. 1. Draw circle (arc) P, center P, any radius, intersecting the line in two points. P 2. Label the points A and B. 3. Draw circle A, center A, radius AP and circle B, center B, radius BP. A B 4. Label C, the intersection of circles A and B. 5. Draw line PC. C 7. Construct a right angle with vertex P. P 8. Construct a line parallel to the given line through the given point P. P 9. In the space below to the right , construct and label≮ABC whose measure is one-half the measure of≮UVW. A U V B W 0 10. Construct and label ≮RST which measures 45 . 45° S C 11. Construct and label equilateral ΔCDE such that CD = 2AB. D A C B E 12. Solve for x and y. Show work. 4x 10 = 90 y = 180 24 4x = 100 y = 156 240 y x = 25 4x 10 y 13. Construct three more equilateral triangles that each share a side withΔABC. C A B 14. True or false? If false, correct the sentence so that it is always true. F Alternate interior angles are equal. a) ____ If parallel lines are cut by a transversal, alternate interior angles are =. 0 F b) ____The sum of an angle and its supplement is 90o. 180 cannot F A scalene triangle could be isosceles. c) ____ 180o F The sum of theadjacent angles on one side of a line is 3600. d) ____ T A line segment has an infinite number of bisectors. e) ____ 15. State the reason that justifies the statement. a) m≮ABC = m≮ABD + m≮DBC Angle Addition Postulate C D diagram for a. B A b) m≮VSB = m≮LBS If ll lines are cut by a transversal, alternate interior angles are equal. R c) m≮RST = m≮SBL If ll lines are cut by a transversal, corresponding angles are equal. T S V diagram for d) m≮RST = m≮VSB b - e. L B Vertical angles are equal. 0 e) m≮TSR + m≮RSV = 180 Angles that form a linear pair sum to 180o. 16. Fill in the blanks. line a) Collinear points are points that lie on the same ___________. half plane b) A ________-_________ is the set of all points in a plane on one side of a line. equiangular (all angles equal) c) A regular polygon is both equilateral and _____________________. Deductive d) _________________reasoning is reasoning based on observations and accepted facts. e - h Fill in a number. 0 midpoint(s). e) A line has ____ 1 perpendicular bisector(s). f) A segment has _____ 1 midpoint(s). g) A segment has ____ 1 bisector(s). h) An angle has ____ 17. Solve for y. Show work. 5y 2y30 y+102 7y 30 = y + 102 (Exterior angle Th.) 6y = 132 y = 22