Polygon Definition and Classification
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 3: Angles and Triangles) learn to define and classify polygons as convex or concave. A polygon is a closed figure with three or more straight sides; convex polygons have all interior angles less than 180 degrees, while concave polygons have at least one angle greater than 180 degrees.
Key Concepts
A polygon is a closed plane figure formed by three or more line segments that meet only at their endpoints. Polygons are classified as convex if all line segments connecting any two vertices lie inside the polygon, or concave if at least one line segment connecting two vertices lies outside the polygon.
Common Questions
What is a polygon in 7th grade geometry?
A polygon is a closed plane figure formed by three or more line segments that meet only at their endpoints. Examples include triangles, quadrilaterals, pentagons, and hexagons.
What is the difference between a convex and concave polygon?
A convex polygon has all interior angles less than 180 degrees (all vertices point outward). A concave polygon has at least one interior angle greater than 180 degrees (at least one vertex points inward).
How do you classify a polygon as convex or concave?
Check if any interior angle exceeds 180 degrees. If all angles are less than 180, it is convex. If any angle exceeds 180, it is concave (has an inward dent).
What chapter in Big Ideas Math Advanced 2 covers polygon definition and classification?
Chapter 3: Angles and Triangles in Big Ideas Math Advanced 2 (Grade 7) covers polygon definition and classification.
Is a triangle always convex?
Yes. Triangles always have all three interior angles summing to 180 degrees, so each angle must be less than 180 degrees, making all triangles convex.