# 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 .
• 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 .
• DA polygon is convex if some of its vertices point βinward,β 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 , , , , and .

Decide whether 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 , , , , , and . Decide whether is convex or concave.

• AConcave
• BConvex