Grade 7 Workbook — Chapter 14: Quadrilaterals and Their Properties

SOL 7.MG.3 · Companion to Textbook Chapter 14

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Item numbers match the textbook exactly.

PAGE 1 — Chapter opener

Chapter 14 · Quadrilaterals and Their Properties

Standard 7.MG.3

In this chapter you will:

• Compare the sides, angles, diagonals, and lines of symmetry of five named quadrilaterals
• Sort and classify quadrilaterals from their properties
• Give the most specific name for a figure
• Find unknown angle measures using the $360°$ angle sum and parallelogram properties
• Find unknown side lengths using congruent sides and bisected diagonals

Words to know: quadrilateral · vertex · diagonal · parallel · perpendicular · congruent · line of symmetry · parallelogram · rectangle · rhombus · square · trapezoid · isosceles trapezoid · base · leg · bisect · supplementary · perimeter

How this book defines a trapezoid. A trapezoid has exactly one pair of parallel sides. So no parallelogram is a trapezoid, and no trapezoid is a parallelogram. Use this definition on every page.

Markings decoder. Matching hash marks $=$ congruent segments. Matching arrowheads $=$ parallel sides. A small square in a corner $=$ a right angle.

PAGE 2 — The five named quadrilaterals

14.1 The Five Named Quadrilaterals

FIGURE: fig1-five-quadrilaterals.png (full width)

Complete the property table.

Guided practice.

1. Parallelogram $ABCD$.

   Parallel: $\overline{AB} \parallel$ ______ and $\overline{BC} \parallel$ ______

   Congruent: $\overline{AB} \cong$ ______ and $\overline{BC} \cong$ ______

2. Rectangle $EFGH$. Number of right angles: ______

   Congruent sides: ______ $\cong$ ______ and ______ $\cong$ ______

3. Square $JKLM$. Three properties you can read from the markings:

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4. Rhombus $NPQR$. All four sides congruent? ______ All four angles congruent? ______

   Explain the difference: _______________________________________________

5. Isosceles trapezoid $STUV$. Parallel sides: ______ and ______ Congruent legs: ______ and ______

PAGE 3 — Diagonals

What the Diagonals Tell You

FIGURE: fig3-diagonals.png (full width)

Independent practice.

6. Write yes (always) or no (not always) in every cell.

   Figure	Diagonals bisect each other	Diagonals congruent	Diagonals perpendicular
   Parallelogram
   Rectangle
   Rhombus
   Square

Do not over-claim. A parallelogram's diagonals bisect each other. They are congruent only if it is a rectangle, and perpendicular only if it is a rhombus.

PAGE 4 — Lines of symmetry

Fold It and Count

FIGURE: fig4-lines-of-symmetry.png (full width)

Draw every line of symmetry. Sketch each figure in the box, then draw each fold line as a dashed line and write the count.

Independent practice, continued.

7. Lines of symmetry: square ______ · rectangle (not a square) ______ · rhombus (not a square) ______ · parallelogram (neither) ______ · isosceles trapezoid ______

8. Which of the five named quadrilaterals always have four right angles? ____________________

9. Which of the five named quadrilaterals always have four congruent sides? ____________________

10. The diagonals of a rhombus meet at $X$. $m\angle$ at $X =$ ______ Property used: ____________________

11. Application. A window frame meant to be a rectangle has diagonals measuring $60$ in and $62$ in.

    What does this tell the carpenter? _______________________________________________

    Property used: _______________________________________________

12. Reasoning. Why does a parallelogram that is neither a rectangle nor a rhombus have no lines of symmetry?

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PAGE 5 — Exit ticket 14.1

Exit Ticket · Lesson 14.1

Name: ________________________ Date: ____________

13. Which named quadrilaterals always have perpendicular diagonals? ____________________

14. Lines of symmetry in a rectangle that is not a square: ______ Where are they? ____________________

15. True or false: in every parallelogram the diagonals are congruent. ______

    If false, correct it: _______________________________________________

16. Explain the difference between parallel and congruent, and name a quadrilateral in which both are true of the same pair of sides.

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PAGE 6 — The classification hierarchy

14.2 Sorting and Classifying Quadrilaterals

FIGURE: fig2-classification-hierarchy.png (full width)

Complete each sentence.

Every rectangle, rhombus, and square is a ______________.

A square is both a ______________ and a ______________.

A parallelogram is ______ (always / not always) a rectangle.

Under this book's definition, a trapezoid has ______________ one pair of parallel sides, so a parallelogram ______ (is / is not) a trapezoid.

Guided practice. Write T or F and give a reason.

17. Every square is a rectangle. ______ Reason: ____________________________________

18. Every rectangle is a square. ______ Reason: ____________________________________

19. Every rhombus is a parallelogram. ______ Reason: ____________________________________

20. Is a parallelogram a trapezoid? ______ Reason: ____________________________________

21. Four congruent sides and four right angles. Most specific name: ____________________

PAGE 7 — Sorting by clues

Give the MOST Specific Name

22. Fill in the most specific name for each set of clues.

    Clues	Most specific name
    a) Opposite sides parallel; four right angles; sides $5$, $9$, $5$, $9$
    b) Four congruent sides; no right angles
    c) Exactly one pair of parallel sides; congruent legs
    d) Opposite sides parallel; diagonals bisect but are neither congruent nor perpendicular

23. Every name that applies to a square. Circle all that apply:

    quadrilateral · parallelogram · rectangle · rhombus · trapezoid

24. Which figures have exactly two lines of symmetry, and where are those lines?

    ____________________________ Lines: ____________________________

    ____________________________ Lines: ____________________________

25. Diagonals bisect each other and are perpendicular, but not congruent. Most specific name: ____________________

26. Diagonals bisect each other and are congruent, but not perpendicular. Most specific name: ____________________

PAGE 8 — Apply and reason

Classification in Context

27. Application. A floor tile has four congruent sides. Its diagonals cross at a right angle, and one diagonal is longer than the other.

    Most specific name: ____________________

    Which clue rules out "square"? _______________________________________________

28. Reasoning. Marisol says, "A rhombus is never a rectangle."

    When is she right? _______________________________________________

    When is she wrong? _______________________________________________

    Example for each: _______________________________________________

PAGE 9 — Exit ticket 14.2

Exit Ticket · Lesson 14.2

Name: ________________________ Date: ____________

29. Four right angles and sides $6$, $6$, $6$, $6$. Most specific name: ____________________

30. Is every parallelogram a rhombus? ______ Counterexample: ____________________

31. Can a quadrilateral be both a trapezoid and a parallelogram in this book? ______

    Why? _______________________________________________

32. Why is "most specific name" a fairer question than "what shape is this?"

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PAGE 10 — Why $360°$

14.3 Finding Unknown Angle Measures

FIGURE: fig5-angle-sum-two-triangles.png (full width)

One diagonal splits any quadrilateral into ______ triangles.

Each triangle's angles add to ______°, so the quadrilateral's four angles add to ______°.

FIGURE: fig6-parallelogram-angles.png (full width)

In a parallelogram: opposite angles are ______________ and consecutive angles are ______________ (they add to ______°).

Guided practice.

33. Quadrilateral $WXYZ$: $85° + 100° + 70° +$ ______ $= 360°$, so $x =$ ______

34. Parallelogram $ABCD$ with $m\angle A = 62°$.

    $x =$ ______ Property: ____________________

    $y =$ ______ Property: ____________________

    $z =$ ______ Property: ____________________

    Check: ______ $+$ ______ $+$ ______ $+$ ______ $= 360°$

35. FIGURE: fig7-unknown-angles.png (full width)

    Isosceles trapezoid $PQRS$ with $m\angle P = 63°$: $n = m\angle S =$ ______ $m\angle Q =$ ______ $m\angle R =$ ______

36. Angles $112°$, $68°$, $95°$. Fourth angle: ______

37. One angle of a parallelogram is $90°$. Other three: ______, ______, ______ Most specific name: ____________________

PAGE 11 — Angle practice

Angle Computation Frames

Independent practice.

38. Missing angle measure.

    a) $100° + 80° + 100° +$ ______ $= 360°$ → ______

    b) $55° + 125° + 55° +$ ______ $= 360°$ → ______

    c) $90° + 90° + 130° +$ ______ $= 360°$ → ______

39. Parallelogram $ABCD$, $m\angle A = 47°$. $m\angle B =$ ______ $m\angle C =$ ______ $m\angle D =$ ______

40. Parallelogram $ABCD$, $m\angle A = (3x + 5)°$ and $m\angle B = (2x)°$.

    Equation: ____________________________

    $x =$ ______ $m\angle A =$ ______ $m\angle B =$ ______

41. One angle of a rhombus is $108°$. Others: ______, ______, ______

    Why does a rhombus follow parallelogram angle rules? ____________________________

42. Isosceles trapezoid with a base angle of $74°$. Other three: ______, ______, ______

PAGE 12 — Apply and reason

Angles in Context

43. Application. A skateboard ramp side panel is a right trapezoid: two right angles, and the sloped front makes a $68°$ angle with the ground.

    Equation: ____________________________ Fourth angle: ______°

44. Reasoning. Why does one angle determine all four angles of a parallelogram, but not of a general quadrilateral?

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PAGE 13 — Exit ticket 14.3

Exit Ticket · Lesson 14.3

Name: ________________________ Date: ____________

45. Angles $78°$, $102°$, $61°$. Fourth: ______

46. Parallelogram $PQRS$, $m\angle Q = 115°$. $m\angle P =$ ______ $m\angle R =$ ______ $m\angle S =$ ______

47. Isosceles trapezoid with a base angle of $82°$. The two angles at the other base: ______ and ______

48. Explain with two triangles why the four angles of any quadrilateral add to $360°$.

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PAGE 14 — Sides you can copy

14.4 Finding Unknown Side Lengths

FIGURE: fig8-unknown-sides.png (full width)

Fill in the property.

In a parallelogram, ______________ sides are congruent.

In a rhombus or square, ______ sides are congruent.

In a rectangle, the diagonals are ______________.

In an isosceles trapezoid, the ______________ are congruent.

In any parallelogram, the diagonals ______________ each other.

Guided practice.

49. Parallelogram $ABCD$: $2x + 3 =$ ______ $x =$ ______ $m = AD =$ ______

50. Rhombus $EFGH$: $3y - 1 =$ ______ $y =$ ______ Each side: ______ Perimeter: ______

51. Rectangle $JKLM$: $p = KN =$ ______ $JL =$ ______

52. Parallelogram with sides $13$ and $8$. Perimeter: ______

53. Square with perimeter $52$. Side: ______

PAGE 15 — Side computation frames

Solve for the Unknown Length

Independent practice.

54. Parallelogram $ABCD$, $AB = 5x$, $DC = 35$.

    Equation: ____________________ $x =$ ______ $AB =$ ______

55. Rhombus with sides $4t + 3$ and $23$.

    Equation: ____________________ $t =$ ______ Perimeter: ______

56. Parallelogram $ABCD$, diagonals meet at $M$: $AM = 9$, $BM = 6x$, $MD = 18$.

    $x =$ ______ $AC =$ ______ $BD =$ ______

57. Rectangle $ABCD$: $AC = 5n$, $BD = 30$.

    $n =$ ______ One half-diagonal: ______

58. Isosceles trapezoid: legs $3w$ and $21$; bases $26$ and $14$.

    $w =$ ______ Perimeter: ______

PAGE 16 — Apply and reason

Side Lengths in Context

59. Application. A rectangular garden gate has a diagonal brace of $91$ in. A second brace runs along the other diagonal.

    Length needed: ______ in Property used: ____________________________

60. Reasoning. Why does one side of a rhombus give you the perimeter, while one side of a parallelogram does not?

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PAGE 17 — Exit ticket 14.4

Exit Ticket · Lesson 14.4

Name: ________________________ Date: ____________

61. Parallelogram $ABCD$, $AB = 3x + 4$, $DC = 22$. $x =$ ______

62. Rhombus with side $9$. Perimeter: ______

63. Rectangle $ABCD$, diagonals meet at $N$, $AN = 11$. $BD =$ ______

64. Only $\overline{BC}$ is labeled in parallelogram $ABCD$, with $BC = 14$. Why is $AD = 14$?

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PAGE 18 — Review Part A

Chapter 14 Review · Properties (7.MG.3a)

65. Always both pairs of opposite sides parallel: ____________________________

66. Always four congruent sides: ____________________________

67. Always four right angles: ____________________________

68. Diagonals always bisect each other? Parallelogram ______ Rectangle ______ Rhombus ______ Square ______

69. Always congruent diagonals: ____________________________

70. Always perpendicular diagonals: ____________________________

71. Lines of symmetry: square ______ · rectangle (not a square) ______ · rhombus (not a square) ______ · parallelogram (neither) ______ · isosceles trapezoid ______

72. Two properties every rhombus has that a general parallelogram does not:

    ____________________________ and ____________________________

PAGE 19 — Review Part B

Chapter 14 Review · Sorting and Classifying (7.MG.3b)

73. Four congruent sides and four right angles: ____________________

74. Diagonals bisect and are congruent; sides $8$, $5$, $8$, $5$: ____________________

75. Exactly one pair of parallel sides, congruent legs: ____________________

76. Circle every name that applies to every square:

    quadrilateral · parallelogram · rectangle · rhombus · trapezoid

77. Every parallelogram is a rectangle. T / F Reason: ____________________________

78. Every square is a rhombus. T / F Reason: ____________________________

79. Is a rectangle a trapezoid in this book? ______ Why? ____________________________

80. Diagonals bisect and are perpendicular but not congruent: ____________________

PAGE 20 — Review Part C

Chapter 14 Review · Unknown Angles (7.MG.3c)

81. Angles $96°$, $84°$, $113°$. Fourth: ______

82. Parallelogram $ABCD$, $m\angle A = 54°$. $m\angle B =$ ______ $m\angle C =$ ______ $m\angle D =$ ______

83. Isosceles trapezoid, one base angle $71°$. Other three: ______, ______, ______

84. Consecutive angles $(4x)°$ and $(5x)°$.

    Equation: ____________________ $x =$ ______ Angles: ______ and ______

85. One angle of a rhombus is $124°$. Others: ______, ______, ______

86. Right trapezoid with two right angles and a $55°$ angle. Fourth: ______

PAGE 21 — Review Part D

Chapter 14 Review · Unknown Sides (7.MG.3d)

87. Parallelogram $ABCD$, $AB = 4x - 5$, $DC = 27$. $x =$ ______

88. Rhombus with sides $6y$ and $30$. $y =$ ______ Perimeter: ______

89. Parallelogram diagonals meet at $M$: $AM = 2z$, $MC = 14$. $z =$ ______ $AC =$ ______

90. Rectangle $ABCD$, $AC = 34$, diagonals meet at $M$. $BD =$ ______ $AM =$ ______

91. Isosceles trapezoid: legs $5k$ and $35$; bases $40$ and $24$. $k =$ ______ Perimeter: ______

PAGE 22 — Review Part E

Chapter 14 Review · Application and Reasoning

92. Application. A quilt block is a rhombus with side $7$ in and one angle of $116°$.

    Perimeter: ______ in All four angles: ______, ______, ______, ______

93. Application. A rectangular window frame has one diagonal measuring $80$ in.

    The other diagonal should measure: ______ in

    What would a measurement of $78$ in mean? _______________________________________________

94. Reasoning. Why is every square a rectangle, but not every rectangle a square?

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95. Reasoning. A student says any quadrilateral with two pairs of congruent sides must be a parallelogram.

    Counterexample: ____________________________

    What was overlooked? _______________________________________________

96. Reasoning. You can see only the two diagonals of a quadrilateral and how they cross. How do you tell a rectangle, a rhombus, and a square apart?

    Rectangle: ____________________________

    Rhombus: ____________________________

    Square: ____________________________

Canva production notes

• Page size: 8.5 × 11 in, 0.75 in margins
• Type: headings 24–28 pt, body 12–14 pt, answer blanks 14 pt with 1.5 line spacing
• Figure widths: fig1-five-quadrilaterals.png, fig3-diagonals.png, fig4-lines-of-symmetry.png, and fig8-unknown-sides.png are wide landscape strips — place full width across the page. fig2-classification-hierarchy.png and fig5-angle-sum-two-triangles.png are closer to landscape rectangles; place full width with generous space beneath. fig6-parallelogram-angles.png and fig7-unknown-angles.png sit well at about 75 percent width, centered.
• Symmetry sketch table on page 4: make each sketch cell at least 1.75 in tall and square-ish so students have room to draw a shape and its fold lines; a light dot grid inside the cells helps students draw straight fold lines
• Property tables: set a fixed row height so "not always" fits on one line without wrapping
• Angle and side frames: keep each equation and its blank inside one text box so the layout does not reflow
• Answer blanks: keep every blank on the same line as its prompt