ssrs barcode font Prove that three or more parallel lines divide any two transversals proportionately. in Objective-C

Generation QR in Objective-C Prove that three or more parallel lines divide any two transversals proportionately.

7.23. Prove that three or more parallel lines divide any two transversals proportionately.
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(7.16)
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7.24. In similar triangles ABC and A B C of Fig. 7-49, /B and /B are corresponding angles. Find m/B if (a) m/A 120 and m/C 25 ; (b) m/A m/C 127 . (7.17)
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CHAPTER 7 Similarity
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7.25. In similar triangles ABC and A B C of Fig. 7-50, /A > /A and /B > /B . (a) Find a if c a 20; (c) find c if b 63.
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24; (b) find b if (7.17)
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Fig. 7-49
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Fig. 7-50
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7.26. In each part of Fig. 7-51, show that the indicated triangles are similar.
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(7.18)
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Fig. 7-51
7.27. In each part of Fig. 7-52, two pairs of congruent angles can be used to prove the indicated triangles similar. Find the congruent angles. (7.18)
AB is a tangent
Fig. 7-52
7.28. In each part of Fig. 7-53, determine the angles that can be used to prove the indicated triangles similar.
(7.19)
CHAPTER 7 Similarity
Fig. 7-53
7.29. In each part of Fig. 7-54, determine the pair of congruent angles and the proportion needed to prove the indicated triangles similar. (7.20)
Fig. 7-54
7.30. In each part of Fig. 7-55, state the proportion needed to prove the indicated triangles similar.
(7.21)
Fig. 7-55
7.31. In each part of Fig. 7-56, prove the indicated proportion.
(7.25)
Fig. 7-56
7.32. In nABC (Fig. 7-57), DE i BC.
CHAPTER 7 Similarity
(7.22)
Fig. 7-57
(a) Let a (b) Let c (c) Let a
4, AB 5, AC 7, p
8, p 15, q 11, q
10. Find q. (d) Let b 24. Find p. (e) Let a 22. Find b. (f) Let c
9, p 10, p 3, p
20, q 24, q 4, q
35. Find a. 84. Find AB. 7. Find d. (7.22)
7.33. Find x in each part of Fig. 7-58.
Fig. 7-58
7.34. A 7-ft upright pole near a vertical tree casts a 6-ft shadow. At that same time, find (a) the height of the tree if its shadow is 36 ft long; (b) the length of the shadow of the tree if its height is 77 ft. (7.23) 7.35. Prove each of the following: (a) In nABC, if AD and CE are altitudes, then AD :CE AB :BC. (7.23)
(b) In circle O, diameter AB and tangent BC are sides of nABC. If AC intersects the circle in D, then AD:AB AB : AC. (c) The diagonals of a trapezoid divide each other into proportional segments. (d) In right nABC, CD is the altitude to the hypotenuse AB, then AC:CD 7.36. Prove each of the following: (a) A line parallel to one side of a triangle cuts off a triangle similar to the given triangle. (b) Isosceles right triangles are similar to each other. (c) Equilateral triangles are similar to each other. (d) The bases of a trapezoid form similar triangles with the segments of the diagonals. 7.37. Complete each of the following statements: (7.26) AB :BC. (7.24)
(a) In similar triangles, if corresponding sides are in the ratio 8:5, then corresponding altitudes are in the ratio . (b) In similar triangles, if corresponding angle bisectors are in the ratio 3:5, then their perimeters are in the ratio . (c) If the sides of a triangle are halved, then the perimeter is , the angle bisectors are , the medians are , and the radii of the circumscribed circle are .
CHAPTER 7 Similarity
7.38. (a) Corresponding sides of two similar triangles have lengths 18 and 12. If an altitude of the smaller has length 10, find the length of the corresponding altitude of the larger. (7.26) (b) Corresponding medians of two similar triangles have lengths 25 and 15. Find the perimeter of the larger if the perimeter of the smaller is 36. (c) The sides of a triangle have lengths 5, 7, and 8. If the perimeter of a similar triangle is 100, find its sides. (d) The bases of a trapezoid have lengths 5 and 20, and the altitude has length 12. Find the length of the altitude of the triangle formed by the shorter base and the nonparallel sides extended to meet. (e) The bases of a trapezoid have lengths 11 and 22. Its altitude has length 9. Find the distance from the point of intersection of the diagonals to each of the bases. 7.39. Complete each of the following statements: (7.27)
(a) If corresponding sides of two similar polygons are in the ratio 3: 7, then the ratio of their corresponding altitudes is . (b) If the perimeters of two similar hexagons are in the ratio of 56 to 16, then the ratio of their corresponding diagonals is . (c) If each side of an octagon is quadrupled and the angles remain the same, then its perimeter is . (d) The base of a rectangle is twice that of a similar rectangle. If the radius of the circumscribed circle of the first rectangle is 14, then the radius of the circumscribed circle of the second is . 7.40. Prove each of the following: (a) Corresponding angle bisectors of two triangles have the same ratio as a pair of corresponding sides. (b) Corresponding medians of similar triangles have the same ratio as a pair of corresponding sides. 7.41. Provide the proofs requested in Fig. 7-59. (7.28) (7.28)
Fig. 7-59
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