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(a) a a (b) a b b b a 88 36 90 2b Ans. Ans. 62 and 26 60 and 30 (c) a a (d) a a b 180 2b 60 b b 180 24 Ans. Ans. 100 and 80 78 and 102
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1.1. Point, line, and plane are undefined terms. Which of these is illustrated by (a) the tip of a sharpened pencil; (b) the shaving edge of a blade; (c) a sheet of paper; (d) a side of a box; (e) the crease of a folded paper; (f) the junction of two roads on a map (1.1) 1.2. (a) Name the line segments that intersect at E in Fig. 1-49. (b) Name the line segments that intersect at D. (c) What other line segments can be drawn using points A, B, C, D, E, and F (d) Name the point of intersection of AC and BD. (1.2)
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Fig. 1-49
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Fig. 1-50
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1.3. (a) Find the length of AB in Fig. 1-50 if AD is 8 and D is the midpoint of AB (b) Find the length of AE if AC is 21 and E is the midpoint of AC. 1.4. (a) Find OB in Fig. 1-51 if diameter AD 36.
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(1.3)
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(1.4)
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(b) Find the number of degrees in AE if E is the midpoint of semicircle AED. Find the number of degrees in (c) CD; (d ) AC ; (e) AEC.
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Fig. 1-51
Fig. 1-52
CHAPTER 1 Lines, Angles, and Triangles
1.5. Name the following angles in Fig. 1-52 (a) an acute angle at B; (b) an acute angle at E; (c) a right angle; (d) three obtuse angles; (e) a straight angle. (1.5) 1.6. (a) Find m/ADC if m/c (b) Find m/AEB if m/e (c) Find m/EBD if m/a (d) Find m/ABC if m/b 45 and m/d 60 . 15 . 42 . 85 in Fig. 1-53. (1.6)
Fig. 1-53
5 2 1 1 1.7. Find (a) 6 of a rt. /; (b) 9 of a st. /; (c) 3 of 31 ; (d) 5 of 45 55 . 1
(1.7)
1.8. What turn or rotation is made (a) by an hour hand in 3 hours; (b) by the minute hand in 3 of an hour What rotation is needed to turn from (c) west to northeast in a clockwise direction; (d) east to south in a counterclockwise direction; (e) southwest to northeast in either direction (1.8) 1.9. Find the angle formed by the hand of a clock (a) at 3 o clock; (b) at 10 o clock; (c) at 5:30 AM; (d) at 11:30 PM. 1.10. In Fig. 1-54: (a) Name two pairs of perpendicular lines. (b) Find m/BCD if m/4 is 39 . If m/1 78 , find (c) m/BAD; (d) m/2; (e) m/CAE.
(1.9) (1.10)
Fig. 1-54
Fig. 1-55
1.11. (a) In Fig. 1-55(a), name three right triangles and the hypotenuse and legs of each.
(1.11)
In Fig. 1-55(b), (b) name two obtuse triangles and (c) name two isosceles triangles, also naming the legs, base, and vertex angle of each. 1.12. In Fig. 1-56, name the congruent lines and angles (a) if PR is a ' bisector of AB; (b) if BF bisects /ABC; (c) if CG is an altitude to AD; (d) if EM is a median to AD. (1.12)
Fig. 1-56
CHAPTER 1 Lines, Angles, and Triangles
1.13. In Fig. 1-57, state the relationship between: (a) /1 and /4 (b) /3 and /4 (c) /1 and /2 (d) /4 and /5 (e) /1 and /3 (f) /AOD and /5
(1.13)
Fig. 1-57
1.14. Find two angles such that:
(1.14)
(a) The angles are complementary and the measure of the smaller is 40 less than the measure of the larger. (b) The angles are complementary and the measure of the larger is four times the measure of the smaller. (c) The angles are supplementary and the measure of the smaller is one-half the measure of the larger. (d) The angles are supplementary and the measure of the larger is 58 more than the measure of the smaller. (e) The angles are supplementary and the measure of the larger is 20 less than three times the measure of the smaller. (f) The angles are adjacent and form an angle measuring 140 . The measure of the smaller is 28 less than the measure of the larger. (g) The angles are vertical and supplementary. 1.15. For each of the following, let the two angles be represented by a and b. Obtain two equations for each case, and then find the angles. (1.15) (a) The angles are adjacent and form an angle measuring 75 . Their difference is 21 . (b) The angles are complementary. One measures 10 less than three times the other. (c) The angles are supplementary. One measures 20 more than four times the other.
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