Geometric diagram conventions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading marks in a geometry diagram

Mathematics · Geometry · ages 9-12
Name ______________________   Date ____________

  1. In a geometry diagram, what does a small square drawn inside the corner where two lines meet tell you?

    • The two lines are the same length
    • The angle there is a right angle, 90 degrees
    • The angle is smaller than 90 degrees

  2. In a diagram, a small square is drawn inside the corner between two lines. What angle is that?

    • A right angle (90°)
    • A wide angle (more than 90°)
    • An angle that hasn't been measured yet

  3. Angle ABC has its vertex, or corner point, at B.

    Circle one:   True   False

  4. A diagram shows two sides of a shape, each with a single tick mark. What does that tell you?

    • The two sides are equal in length
    • The two sides are parallel
    • The two sides meet at a right angle

  5. A diagram shows two sides with single tick marks and two other sides with no tick marks at all. The marks prove the two unmarked sides are equal to each other.

    Circle one:   True   False

  6. A diagram shows a quadrilateral with one tick mark on each of its four sides and a small square in one corner. What do the marks tell you?

    • All four sides are equal, and one angle is 90 degrees
    • All four sides are equal, but no angle is marked
    • Only two sides are equal, and one angle is 90 degrees

  7. A diagram shows a small square symbol inside the corner of two lines. What is the size of that angle?

    • 45°
    • 90°
    • 180°

  8. A shape has two sides with a single tick mark and two other sides with a double tick mark. What do the marks guarantee?

    • The single-tick sides are equal to each other, and separately the double-tick sides are equal to each other
    • All four of those sides are exactly the same length
    • The double ticks mean that pair is longer than the single-tick pair

  9. Angle PQR and angle STU share matching double-arc marks. Angle STU is marked 65 degrees. Which letter names the vertex of angle PQR, and what is its measure?

    • Vertex P, 65 degrees
    • Vertex Q, 65 degrees
    • Vertex Q, 115 degrees

  10. In a shape, sides AB and BC both have a single tick mark. Side CD has a double tick mark. Which side is guaranteed by the marks to equal AB?

    • CD
    • Both BC and CD
    • BC
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading marks in a geometry diagram W1-mt_e4V6hvcuEJ-s1

  1. The angle there is a right angle, 90 degrees · The small square is the standard symbol for a right angle.
  2. A right angle (90°) · A small square drawn inside an angle always marks a right angle, which is exactly 90°.
  3. True · The middle letter in three-letter angle notation always names the vertex. A and C name points on the arms.
  4. The two sides are equal in length · Matching tick marks are a shortcut for 'these lengths are equal', so you do not need to measure them.
  5. False · Tick marks only guarantee equal lengths within a marked group. Unmarked sides have no mark to compare. Their relation to each other and to the marked sides is unknown.
  6. All four sides are equal, and one angle is 90 degrees · One tick mark on each side means all four sides are equal. The small square in the corner means that angle is 90 degrees.
  7. 90° · The small square symbol is a fixed rule for a right angle, which measures 90° every time.
  8. The single-tick sides are equal to each other, and separately the double-tick sides are equal to each other · Same tick count guarantees equal lengths within each group. The single-tick sides are equal to each other. The double-tick sides are equal to each other. Different counts give no determined cross-group relation.
  9. Vertex Q, 65 degrees · The middle letter Q is the vertex of angle PQR. Matching double-arc marks identify equal angles. Since angle STU is 65 degrees, angle PQR is also 65 degrees.
  10. BC · AB and BC share the same single tick mark, so they are guaranteed equal. CD has a different mark. Its relation to AB is unknown.
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