Worksheet: Convex and Concave Polygons

In this worksheet, we will practice classifying polygons as convex or concave.

Q1:

Consider convex polygons.

Select the definition of a convex polygon.

  • AA polygon is convex if it contains one or more interior angles less than 1 8 0 ∘ .
  • BA polygon is convex if it contains one or more interior angles greater than 1 8 0 ∘ .
  • CA polygon is convex if some of its vertices point β€œinward,” toward the center.
  • DA polygon is convex if all of the line segments drawn between two points, on or inside the polygon, are contained within the polygon.

Which of these properties is true of a convex polygon?

  • ASome of its internal angles are less than 180 degrees.
  • B Some of the diagonals of a convex polygon will lie outside the polygon.
  • CA line drawn through a convex polygon, depending on exactly where you draw it, can intersect the polygon in more than two places.
  • DAll of its internal angles are at most 180 degrees.

Q2:

In a pentagon 𝐴 𝐡 𝐢 𝐷 𝐸 , π‘š ∠ 𝐴 = 1 1 0 ∘ , π‘š ∠ 𝐷 = 6 2 ∘ , π‘š ∠ 𝐸 = 8 9 ∘ , and π‘š ∠ 𝐡 = π‘š ∠ 𝐢 .

Decide whether 𝐴 𝐡 𝐢 𝐷 𝐸 is convex or concave.

  • AThe given information is not enough.
  • BConcave
  • CConvex

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