# 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 βinward,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.
- B
**Some 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.

**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