3-1 Parallel Lines and Transversals. Refer to the figure at the right to identify each of the following. 1. a plane parallel to plane ZWX ANSWER: TUV
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1 Refer to the figure at the right to identify each of the following. Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 1. a plane parallel to plane ZWX TUV 2. a segment skew to that contains point W 3. all segments parallel to 4. CONSTRUCTION Use the diagram of the partially framed storage shed shown to identify each of the following. a. Name three pairs of parallel planes. b. Name three segments parallel to c. Name two segments parallel to. d. Name two pairs of skew segments and 8 alternate exterior 6. 2 and 4 corresponding 7. 3 and 6 alternate interior 8. 6 and 7 consecutive interior Identify the transversal connecting each pair of angles. Then classify the relationship between each pair of angles and 4 line n; corresponding a. plane ABCD plane FGHE; plane ADEF plane BCHG; plane DCHE plane ABGF b. c. Sample answer: and d. Sample answer: and 6 line p ; alternate exterior and 7 line m; consecutive interior esolutions Manual - Powered by Cognero Page 1
2 12. 2 and 7 line p ; alternate interior Refer to the figure to identify each of the following. 20. a segment skew to through point E APPLY MATH Identify the transversal connecting each pair of angles. Then classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 13. all segments parallel to 14. a plane parallel to plane ACD JLM 15. a segment skew to 16. all planes intersecting plane EDM DCL, NML, AED, AEN 17. all segments skew to 18. a segment parallel to 19. a segment parallel to through point J and 9 line s; corresponding and 7 line r; consecutive interior and 5 line t; alternate interior and 11 line v; corresponding and 6 line t; alternate exterior and 8 line s; alternate interior esolutions Manual - Powered by Cognero Page 2
3 27. 2 and 3 line t; consecutive interior and 10 line v; alternate exterior and 11 line s; alternate exterior and 11 line v; alternate interior SAFETY Identify the transversal connecting each pair of angles in the photo of a fire escape shown. Then classify the relationship between each pair of angles. Refer to Page and 5 line c; alternate interior and 7 line d or line f; linear pair and 8 line f ; corresponding and 3 line a; alternate interior 37. POWER Power lines are not allowed to intersect. a. What must be the relationship between power lines p and m? Explain your reasoning. b. What is the relationship between line q and lines p and m? Refer to Page 176. a. Sample answer: Since the lines are coplanar and they cannot touch, they are parallel. b. Line q is a transversal of lines p and m. Describe the relationship between each pair of segments as parallel, skew, or intersecting and 2 line a; vertical and 4 line a; consecutive interior 38. parallel esolutions Manual - Powered by Cognero Page 3
4 39. skew 45. ESCALATORS Escalators consist of steps on a continuous loop that is driven by a motor. At the top and bottom of the platform, the steps collapse to provide a level surface for entrance and exit. 40. intersecting parallel skew intersecting 44. ORGANIZE IDEAS The illusion shown is created using squares and straight lines. a. How are and related? Justify your reasoning. b. How are and related? and a. What is the relationship between the treads of the ascending stairs? b. What is the relationship between the treads of the two steps at the top of the incline? c. How do the treads of the steps on the incline of the escalator relate to the treads of the steps on the bottom of the escalator? a. parallel b. coplanar c. skew 46. ORGANIZE IDEAS Plane P contains lines a and b. Line c intersects plane P at point J. Lines a and b are parallel, lines a and c are skew, and lines b and c are not skew. Draw a figure based upon this description. a. The distance between the segments is the same anywhere on the segment. b. is a transversal between esolutions Manual - Powered by Cognero Page 4
5 47. ANALYXE RELATIONSHIPS Suppose points A, B, and C lie in plane P, and points D, E, and F lie in plane Q. Line m contains points D and F and does not intersect plane P. Line n contains points A and E. a. Draw a diagram to represent the situation. b. What is the relationship between planes P and Q? c. What is the relationship between lines m and n? a. 50. WRITING IN MATH Can a pair of planes be described as skew? No; sample answer: From the definition of skew lines, the lines must not intersect and cannot be coplanar. Different planes cannot be coplanar, but they are always parallel or intersecting. Therefore, skew lines must be on planes that are parallel or intersecting. 51. Which angles are consecutive angles? b. parallel c. skew ANALYZE RELATIONSHIPS Plane X and plane Y are parallel and plane Z intersects plane X. Line is in plane X, line is in plane Y, and line is in plane Z. Determine whether each statement is always, sometimes, or never true. Explain. 48. is skew to Sometimes; is either skew or parallel to because the lines will never intersect and are not coplanar. 49. intersects Sometimes; intersects depending on where the planes intersect. A 1 and 5 B 3 and 4 C 4 and 6 D 4 and 5 C 52. In the diagram of a pedestal below, which segments are parallel to each other? F G H J G esolutions Manual - Powered by Cognero Page 5
6 53. ACT/SAT In the diagram, what is the relationship between 4 and 5? A They are alternate exterior angles. B They are alternate interior angles. C They are corresponding angles. D They are consecutive interior angles. E They are vertical angles. A 54. Which is a transversal for 9 and 11? F line a G line b H line c J line d J esolutions Manual - Powered by Cognero Page 6
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ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or. Explain your reasoning. 4. equiangular;
11-4 Translations and Reflections on the Coordinate Plane
1. Triangle MNP is shown on the coordinate plane. Find the coordinates of the vertices of the image of the triangle MNP translated 5 units to the right and 3 units up. 4. Find the coordinates of the vertices
5-2 Verifying Trigonometric Identities
Verify each identity 1 (sec 1) cos = sin sec (1 cos ) = tan 3 sin sin cos 3 = sin 4 csc cos cot = sin 4 5 = cot Page 1 4 5 = cot 6 tan θ csc tan = cot 7 = cot 8 + = csc Page 8 = csc + 9 + tan = sec 10
Lesson 13: Angle Sum of a Triangle
Student Outcomes Students know the Angle Sum Theorem for triangles; the sum of the interior angles of a triangle is always 180. Students present informal arguments to draw conclusions about the angle sum
Chapter 6 Practice Test
Find the sum of the measures of the interior angles of each convex polygon. 1. hexagon A hexagon has six sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.
Parallel Lines and Transversals. Students will learn how to find the measures of alternate interior angles and same-side interior angles.
Parallel Lines and Transversals Students will learn how to find the measures of alternate interior angles and same-side interior angles. Parallel Lines and Transversals When a pair of parallel lines are
3 John likes to experiment with geometric. 4 Which of the following conjectures is true for
1 Rectangle ABCD is drawn on a coordinate plane. Each angle measures 90. The rectangle is reflected across the y axis, translated 9 units down, and then rotated 180 clockwise about the origin. What would
The SAS Postulate requires the same information as the LL Theorem, so it can be used to prove two right triangles congruent.
State whether each sentence is or false. If false, replace the underlined word or phrase to make a sentence. 1. The vertex angles of an isosceles triangle are false; The base angles of an isosceles triangle