Chapter 7 — Answers
Selected answers for Chapter 7: Quadrilaterals, transcribed from the book’s appendix. They are meant for checking your work, not for copying — the book prints answers to selected exercises only.
Back to Chapter 7 · Teacher’s answers: Chapter 7 · Complete key: Answers to Exercises PDF · Printed answers: appendices PDF
Lesson 1 (pages 260–264)
1. Two points determine a line.
3. Addition.
6. The sum of the angles of a quadrilateral is 360°.
9. A quadrilateral each of whose angles is a right angle is a rectangle.
10. Each angle of a rectangle is a right angle.
14. Lines that form right angles are perpendicular.
17. They seem to be parallel and equal.
21. They are equiangular (or each of their angles is a right angle).
26. .
29. 144°.
31. SSS.
37. Triangles, quadrilaterals, and an octagon.
40. Six sides, three diagonals, and four triangles.
43. .
46. 720°.
47. 120°.
50. .
52. Their sum is 360°.
54. They all appear to be smaller.
Lesson 2 (pages 267–269)
2. Point.
3. See if the figure looks exactly the same when it is turned upside down.
4. Three.
5. Yes. The opposite sides of a parallelogram are equal.
8. An exterior angle of a triangle is greater than either remote interior angle.
11. The opposite sides of a parallelogram are parallel.
15. A line segment is bisected if it is divided into two equal segments.
17. The diagonals of a parallelogram bisect each other.
18. Two points are symmetric with respect to a point if it is the midpoint of the line segment connecting them.
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26. 10.
30. About 24°.
32. ∠AEB = , ∠CED = .
35. AD = 2DC.
37. 180.
45. All three.
Lesson 3 (pages 272–275)
1. A quadrilateral is a parallelogram if its opposite sides are equal.
3. Parallel lines form equal corresponding angles.
4. In a plane, if a line is perpendicular to one of two parallel lines, it is also perpendicular to the other.
8. Supplementary interior angles on the same side of a transversal mean that lines are parallel.
13. SAS.
15. A quadrilateral is a parallelogram if its opposite sides are equal.
20. Equal alternate interior angles mean that lines are parallel.
21. A quadrilateral is a parallelogram if two opposite sides are both parallel and equal.
22. Line symmetry. The figure can be folded along a vertical line so that the two halves coincide.
26. No. Line symmetry (one vertical line).
29. They seem to be parallel.
32. The pairs of opposite angles.
37. A quadrilateral is a parallelogram if its diagonals bisect each other.
39. SSS.
43. A quadrilateral is a rectangle if all of its angles are equal.
47. 12.
53. They are the sides of the quadrilaterals above and below the braced square.
Lesson 4 (pages 277–280)
1. 12.
2. Three.
5. 15.
7. All of the angles of a rectangle are equal.
10. A quadrilateral is a parallelogram if its opposite sides are equal.
12. All rectangles are parallelograms.
17. All of the sides of a rhombus are equal.
19. Two consecutive sides.
24. No. It must be a rectangle.
31. A quadrilateral is a parallelogram if its opposite sides are equal.
34. A quadrilateral all of whose angles are equal is a rectangle.
36. False.
39. True.
43. Its opposite sides are parallel.
Lesson 5 (pages 282–285)
1. A trapezoid.
2. That it has exactly one pair of parallel sides.
4. That all of its angles are right angles (or that they are equal).
5. Yes. All rectangles are parallelograms.
8. Point.
10. They seem to be congruent.
11. Trapezoids.
13. No. The legs of a trapezoid must be equal for it to be isosceles.
16. The bases of a trapezoid are parallel.
17. Through a point not on a line, there is exactly one line parallel to the line.
19. The opposite sides of a parallelogram are equal.
22. If two sides of a triangle are equal, the angles opposite them are equal.
25. Parallel lines form supplementary interior angles with a transversal.
30. The base angles of an isosceles trapezoid are equal.
36. 75°.
40. Parallel lines form equal corresponding angles.
41. 105°.
46. AC and DB bisect each other.
47. A quadrilateral is a parallelogram if its diagonals bisect each other.
49. A trapezoid has only one pair of opposite sides parallel.
Lesson 6 (pages 288–291)
2. A midsegment.
5. , and .
8. A midsegment of a triangle is parallel to the third side.
9. In a plane, two lines parallel to a third line are parallel to each other.
10. A midsegment of a triangle is half as long as the third side.
13. MNPQ is a parallelogram because two opposite sides are both parallel and equal.
17. Addition.
18. Substitution.
20. The sum of its diagonals.
24. ∠A = ∠C because the base angles of an isosceles trapezoid are equal.
28. (4, 7).
29. (8, 10).
32. 5.
35. They should be parallel.
38. They are congruent by SSS.
43. A rhombus.
49. MN seems to be parallel to AB and DC, the bases of the trapezoid.
Review (pages 292–295)
2. Both pairs of its opposite sides are parallel.
4. AAS.
7. Substitution.
9. Four.
13. All of the sides and angles of a square are equal.
16. If a line divides an angle into two equal parts, it bisects the angle.
21. True.
27. True.
31. The sum of the angles of a quadrilateral is 360°.
33. The opposite angles of a parallelogram are equal.
36. D, E, and F.
42. GI ⊥ HM and ML ⊥ HM. In a plane, two lines perpendicular to a third line are parallel.
45. .
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49. A trapezoid.
51. No, because a trapezoid has two parallel sides.
56. IJKL is a trapezoid because .
Algebra Review (page 296)
1. 2.236.
2. 22.36.
3. 223.6.
4. 7.07.
5. 70.7.
6. .
7. .
8. .
9. .
10. .
11. .
12. .
13. .
14. .
15. .
16. .
17. .
18. .
19. .
20. 14.
21. 10.
22. .
23. 11.
24. .
25. 63.
26. .
27. 10.
28. 23.
29. .
30. .
31. .
32. .