1. Basic Construction Pages 37-40 Exercises 9. a. 11; 30 1. 6. b. 30
GEOMETRY LESSON 1-5
Pages Exercises 1. 2. 3. 4. 5.
9. a. 11; 30
b. 30
c. 60
10. 5; 50
11. 15; 48
12. 11; 56
13. 6. 7. 8.
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2. 16. Find a segment on XY so that you can construct YZ as its bisector.
Basic Construction
GEOMETRY LESSON 1-5
14.
15.
16. Find a segment on XY so that you can construct YZ as its bisector.
17. Find a segment on SQ so that you can construct SP as its bisector. Then bisect
PSQ.
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3. 21. Explanations may vary. Samples are given.
Basic Construction
GEOMETRY LESSON 1-5
18. a. CBD; 41
b. 82
c. 49; 49
19. a-b.
20. Locate points A and B on a line. Then construct a at A and B as in Exercise 16.
Construct AD and BC
so that AB = AD = BC.
20. (continued)
21. Explanations may vary. Samples are given.
a. One midpt.; a midpt. divides a segment into two segments. If there were more than one midpt. the segments wouldn’t be .
21. (continued)
b. Infinitely many; there’s only 1 midpt. but there exist infinitely many lines through the midpt. A segment has exactly one bisecting line because there can be only one line to a segment at its midpt.
c. There are an infinite number of lines in space that are to a segment at its midpt. The lines are coplanar.
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4. They appear to meet at one pt.
Basic Construction
GEOMETRY LESSON 1-5
22.
23.
24.
25. They are both correct. If you mult. each side of Lani’s eq. by 2, the result is Denyse’s eq.
26. Open the compass to more than half the measure of the segment. Swing large arcs from the endpts. to intersect above and below the segment. Draw a line through the two pts. where the arcs intersect. The pt. where the line and segment intersect is the midpt. of the segment.
27.
28. a.
They appear to meet at one pt.
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5. c. The three bisectors of a intersect in one pt.
Basic Construction
GEOMETRY LESSON 1-5
33. a.
b. They are all 60°.
c. Answers may vary. Sample: Mark a pt., A. Swing a long arc from A. From a pt. P on the arc, swing another arc the same size that intersects the arc at a second pt., Q. Draw PAQ. To construct a 30° , bisect the 60° .
28. (continued) b.
c. The three bisectors of a intersect in one pt.
29.
30.
31. impossible; the short segments are not long enough to form a .
32. impossible; the short segments are not long enough to form a .
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6. c. Point O is the center of the circle. 36. ; the line intersects.
Basic Construction
GEOMETRY LESSON 1-5
34. a-c.
35. a-b.
35, (continued)
c. Point O is the center of the circle.
; the line intersects.
37. D
38. F
39. [2] a.Draw XY. With the compass pt. on B swing an arc that intersects BA and BC. Label the intersections P and Q, respectively.
With the compass point on X, swing a arc intersecting XY.
39. [2] (continued)
Label the intersection K. Open the compass to PQ. With compass pt. on K, swing an arc to intersect the first arc. Label the intersection R. Draw XR.
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7. 49. No; they do not have the same endpt.
Basic Construction
GEOMETRY LESSON 1-5
41. 6
42. 10
43. 4
44. 3
45.
and 180
48.
49. No; they do not have the same endpt.
50. Yes; they both represent a segment with endpts. R and S.
39. [2] b. With compass open to XK, put compass point on X and swing an arc intersecting XR. With compass on R and open to KR, swing an arc to intersect the first arc. Label intersection T. Draw XT.
[1] one part correct
40. [4] a. Construct its
bisector.
b. Construct the bisector. Then construct the bisector of two new segments.
40. (continued)
c. Draw AB. Do constructions as in parts a and b. Open the compass to the length of the shortest segment in part b.
With the pt. of the compass on B, swing an arc in the opp. direction from A intersecting AB at C. AC = 1.25 (AB).
[3] explanations are not thorough
[2] two explanations correct
[1] part (a) correct
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