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 greater than 180∘.
  • BA polygon is convex if all of the line segments drawn between two points, on or inside the polygon, are contained within the polygon.
  • CA polygon is convex if it contains one or more interior angles less than 180∘.
  • DA polygon is convex if some of its vertices point β€œinward,” toward the center.

Which of these properties is true of a convex polygon?

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

Q2:

In a pentagon 𝐴𝐡𝐢𝐷𝐸, π‘šβˆ π΄=110∘, π‘šβˆ π·=62∘, π‘šβˆ πΈ=89∘, and π‘šβˆ π΅=π‘šβˆ πΆ.

Decide whether 𝐴𝐡𝐢𝐷𝐸 is convex or concave.

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

Q3:

Determine whether the following polygon is convex or concave.

  • AConcave
  • BConvex

Q4:

Determine whether the following polygon is convex or concave.

  • AConvex
  • BConcave

Q5:

Which of the following polygons is convex?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following shapes is a concave polygon?

  • A
  • B
  • C
  • D
  • E

Q7:

Determine whether the polygon given is convex or concave.

  • AConvex
  • BConcave

Q8:

Determine whether the polygon given is convex or concave.

  • AConvex
  • BConcave

Q9:

Which of these properties is true of a concave polygon?

  • AAll of its internal angles are 180 degrees at most.
  • BEach diagonal is lying inside or on the boundary of the polygon.
  • CAll the vertices are pointing outward.
  • DOne or more of its internal angles are more than 180 degrees.
  • EAll its internal angles are more than 180 degrees.

Q10:

In a hexagon 𝐴𝐡𝐢𝐷𝐸𝐹, π‘šβˆ π΄=120∘, π‘šβˆ π΅=109∘, π‘šβˆ πΆ=51∘, π‘šβˆ π·=58∘, and π‘šβˆ πΈ=π‘šβˆ πΉ. Decide whether 𝐴𝐡𝐢𝐷𝐸𝐹 is convex or concave.

  • AConcave
  • BConvex

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