TOPIC 4 Line and Angle Relationships. Good Luck To. DIRECTIONS: Answer each question and show all work in the space provided.
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1 Good Luck To Period Date DIRECTIONS: Answer each question and show all work in the space provided. 1. Name a pair of corresponding angles A. 1 and 4 C. 2 and 7 B. 1 and 5 D. 2 and 4 2. The segment connecting the vertex of a triangle to the midpoint of its opposite side is a(n) A. altitude C. median B. angle bisector D. midsegment 3. In the figure below, what type of angles are 3 and 6? A. alternate exterior angles C. linear pair of angles B. alternate interior angles D. vertical angles Page 1 of 11
2 In the figure below, calculate the measure of 1 and the measure of 2. (Problems 4 and 5) m 1 = 5. m 2 = 6. A flag poll lies perpendicular to a hill and makes a 50 angle as shown below. What is the measure of 1? 50 1 Hill m 1 = Page 2 of 11
3 7. In quadrilateral HIJK, as shown below, HI II KJ. If the measure of H is 62. What is the measure of K? H 62 I K J m K = 8. In the figure below, lines m and n are parallel and are cut by transversal t. What is the value of x? m t n 74 (4x + 22) The value of x is Page 3 of 11
4 9. If p II s, then what is the value of x. (8x + 17) (3x+9) p s The value of x is 10. If x = 14, is p II q? Explain your reasoning. p q 75 7x - (2x - 5) Page 4 of 11
5 Use the figure below for problems Given l ll m. Calculate the measure of each lettered angle. l 120 a b f e c d m 11. a: 12. b: 13. c: 14. d: 15. e: 16. f: Page 5 of 11
6 17. BD bisects ABC the m A?, m ABC = 68, and m BDC = 88 What is A B D m A : C 18. Find the coordinate for midpoint C. 19. Coordinate for point C suur suur AB passes through points A(3, 6), B(-4, 1) and AB coordinates of point D if suur CD passes through C(-5, -3). suur CD. Find the Coordinates of D Page 6 of 11
7 20. Given points M(0, 7), N(-5, 2), and O(-4, -2), find the coordinate of point Q such suuur that MN and OQ suur are perpendicular. Coordinates of Q 21. Use a compass and a straight edge to construct the angle bisector through the given angle below. 22. Use a compass and a straight edge to construct the perpendicular bisector through the given line segment. Page 7 of 11
8 uuur 23. If BE bisects ABD, find m ABE ABE = 24. Complete the following statement: Point F is equidistant from G C B F I D A J H E 25. A revolving sprinkler needs to be set up to water every part of a triangular garden. Where should the sprinkler be located so that it reaches the entire garden but doesn t spray farther than necessary? The sprinkler should be located. Page 8 of 11
9 26. Name the geometric construction 27. Name the geometric construction 28. Name the geometric construction For Problems 29 35: Identify each statement as True (A) or False (B). 29. The circumcenter of a triangle is the center of gravity of the triangular region. 30. In a triangle, an altitude is shorter than either side from the vertex 31. The circumcenter is the intersection of the perpendicular bisectors of the sides of a triangle. 32. The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line. 33. The incenter is equally distant from the three sides of a triangle. 34. In a triangle, if the perpendicular bisector of a side and an altitude coincide, then the triangle is isosceles. 35. The centroid is the intersection of the three medians of a triangle. Page 9 of 11
10 ANSWER KEY Problem Number Answer Standard 1. B. and MA.912.G C. median MA.912.G B. alternate interior angles MA.912.G MA.912.G MA.912.G MA.912.G MA.912.G MA.912.G MA.912.G Yes, since the alternate exterior angles are congruent, then MA.912.G a. 60 MA.912.G b. 60 MA.912.G c. 60 MA.912.G d. 60 MA.912.G e. 60 MA.912.G f. 120 MA.912.G MA.912.G MA.912.G Answers may vary, sample answers: (2, 2)or(0,4/7)or(-12,-8) MA.912.G Answers may vary, sample answers: (-3. -3)or(0,-6)or(-8,2) MA.912.G MA.912.G MA.912.G o MA.912.G Point B and Point C; a point on the perpendicular bisector is MA.912.G.4.2 equidistant from the endpoints of the segment 25. Circumcenter MA.912.G Angle Bisector Construction MA.912.G Parallel Line Construction MA.912.G.2.3 Page 10 of 11
11 ANSWER KEY Problem Number Answer Standard 28. Equilateral Triangle Construction MA.912.G B. False the centroid is the center of gravity MA.912.G B.False the triangle could be a right triangle MA.912.G A. True MA.912.G A. True MA.912.G A. True MA.912.G B. False this is also true in an equilateral triangle MA.912.G A. True MA.912.G.4.2 Page 11 of 11
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