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GEOMETRY TOPIC 4 Line and Angle Relationships Good Luck To ____________________________________________________ Period ________________ Date __________________________ DIRECTIONS: Answer each question and show all work in the space provided. 1. Name a pair of corresponding angles. 2 1 4 3 5 6 7 A. ∠ 1 and ∠ 4 B. ∠ 1 and ∠ 5 8 C. ∠ 2 and ∠ 7 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 B. angle bisector C. median D. midsegment 3. In the figure below, what type of angles are ∠ 3 and ∠ 6? 2 1 3 4 5 6 7 8 A. alternate exterior angles B. alternate interior angles C. linear pair of angles D. vertical angles Page 1 of 11 GEOMETRY TOPIC 4 Line and Angle Relationships In the figure below, calculate the measure of ∠ 1 and the measure of ∠ 2. (Problems 4 and 5) 162° 1 2 4. 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 GEOMETRY TOPIC 4 Line and Angle Relationships 7. In quadrilateral HIJK, as shown below, HI II KJ . If the measure of ∠ H is 62°. What is the measure of ∠ K? I H 62° J K 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 n t 74° (4x + 22)° The value of x is _____ Page 3 of 11 GEOMETRY TOPIC 4 Line and Angle Relationships 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 GEOMETRY TOPIC 4 Line and Angle Relationships Use the figure below for problems 11 -16 Given l ll m. Calculate the measure of each lettered angle. 120° f b a l e c d m 11. a: _________ 12. b: _________ 13. c: _________ 14. d: _________ 15. e: _________ 16. f: __________ Page 5 of 11 GEOMETRY TOPIC 4 Line and Angle Relationships 17. BD bisects ∠ABC , m∠ABC = 68° , and m∠BDC = 88° What is the m∠A ? A D B C m∠A : ______________ 18. Find the coordinate for midpoint C. Coordinate for point C ______________________ 19. suur AB passes through points A(3, 6), B(-4, 1) and coordinates of point D if suur CD suur suur AB || C D . Find the passes through C(-5, -3). Coordinates of D ______________ Page 6 of 11 GEOMETRY TOPIC 4 Line and Angle Relationships 20. Given points M(0, 7), N(-5, 2), and O(-4, -2), find the coordinate of point Q such that suuur MN and suur OQ 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 GEOMETRY TOPIC 4 Line and Angle Relationships uuur 23. If BE bisects ∠ABD , find m ∠ABE ∠ABE = _____ 24. Complete the following statement: Point F is equidistant from _______________ C G B F D I J A 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 GEOMETRY TOPIC 4 Line and Angle Relationships 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 GEOMETRY TOPIC 4 Line and Angle Relationships ANSWER KEY Problem Number 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. Answer B. and C. median B. alternate interior angles 18° 162° 140° 118° 21 14 Yes, since the alternate exterior angles are congruent, then . a. 60° b. 60° c. 60° d. 60° e. 60° f. 120° 54° MA.912.G.1.3 MA.912.G.4.2 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 Answers may vary, sample answers: (2 , 2)or(0,4/7)or(-12,-8) Answers may vary, sample answers: (-3. -3)or(0,-6)or(-8,2) MA.912.G.1.2 MA.912.G.1.2 MA.912.G.8.6 22. 23. 24. 25. 26. 27. Standard MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.1.3 MA.912.G.4.2 MA.912.G.1.1 MA.912.G.8.6 50o Point B and Point C; a point on the perpendicular bisector is equidistant from the endpoints of the segment Circumcenter Angle Bisector Construction Parallel Line Construction MA.912.G.2.3 MA.912.G.4.2 MA.912.G.2.3 MA.912.G.2.3 MA.912.G.2.3 Page 10 of 11 GEOMETRY TOPIC 4 Line and Angle Relationships ANSWER KEY Problem Number 28. 29. 30. 31. 32. 33. 34. 35. Answer Equilateral Triangle Construction B. False – the centroid is the center of gravity B.False – the triangle could be a right triangle A. True A. True A. True B. False – this is also true in an equilateral triangle A. True Standard MA.912.G.2.3 MA.912.G.4.2 MA.912.G.4.2 MA.912.G.4.2 MA.912.G.4.2 MA.912.G.4.2 MA.912.G.4.2 MA.912.G.4.2 Page 11 of 11