Convex and Concave Worksheets

Do you teach geometry to middle or high school students? If so, you're likely always on the lookout for engaging and educational resources to help your students grasp important concepts. Look no further than these convex and concave worksheets! These worksheets are designed to help students understand the difference between convex and concave shapes, and provide ample practice to reinforce their understanding. Whether you're introducing this topic for the first time or reviewing it with your students, these worksheets will be a valuable addition to your teaching materials.

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What is a convex shape?

A convex shape is a geometric shape where all its interior angles are less than 180 degrees, meaning the shape does not have any indentations or concave points. It bulges outward and has a curved or flat surface without any inward curving segments, making it appear smooth and rounded.

Can a convex shape have any concave regions?

No, a convex shape cannot have any concave regions. In a convex shape, any line segment connecting two points on the boundary of the shape lies completely inside it. Concave regions would cause some line segments to cross the boundary, contradicting the definition of a convex shape.

How does a convex shape differ from a concave shape?

A convex shape has all its interior angles less than 180 degrees and all of its sides are pointing outwards, while a concave shape has at least one interior angle greater than 180 degrees and some of its sides are pointing inwards. In simple terms, a convex shape bulges outward, while a concave shape caves inward.

Provide an example of a real-world object that is convex.

A convex object in the real world is a spherical ball, such as a basketball. The outer surface of a basketball curves outward uniformly in all directions, creating a convex shape that bulges outwards.

Is a circle convex or concave? Explain why.

A circle is convex. A convex shape is one where any line segment connecting two points within the shape lies entirely inside the shape. Since a circle has a uniform curvature with no points curving inward, any line segment within the circle will always stay within the boundaries of the circle, making it convex.

What is a concave polygon?

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees, causing the polygon to curve inward at that point. This creates a shape with at least one "dip" or indentation in its boundary, distinguishing it from convex polygons that have all interior angles less than 180 degrees.

Can a concave shape have any convex regions?

No, a concave shape cannot have any convex regions within it. A concave shape is defined by having at least one indentation or curve that bulges inward, while a convex shape bulges outward. Therefore, by definition, a concave shape does not contain any convex regions.

Give an example of a real-world object that is concave.

An example of a real-world object that is concave is a spoon. The inside curve of the spoon's bowl is concave, meaning it curves inward towards the handle. This concave shape allows the spoon to hold and carry liquids more effectively than if it were flat or convex.

Is a crescent moon convex or concave? Explain why.

A crescent moon is concave. This means that it is curved inward, giving it a hollow or "cave-like" appearance. This is because during a crescent moon phase, only a small portion of the Moon's illuminated side is visible from Earth, while the rest remains shrouded in shadow. The curve of the crescent shape appears concave when viewed from our perspective on Earth.

How can you determine if a shape is convex or concave?

To determine if a shape is convex or concave, you can draw a straight line segment connecting any two points within the shape. If the line segment lies entirely within the shape and does not intersect the boundary of the shape more than twice, then the shape is convex. However, if the line segment intersects the boundary of the shape more than twice, then the shape is concave.