Analyze, generalize, and explain properties of polygons using illustrations, including:

• triangles (isosceles, equilateral, scalene, and right triangles)
• quadrilaterals in terms of angle measures, side lengths, diagonal lengths, and angles formed by the intersection of diagonals
• regular polygons.

Explain, using examples, why a given property does or does not apply to certain polygons (e.g., the diagonals of a square are perpendicular, but the diagonals of a rectangle are not even though squares are rectangles).

Identify and explain applications of the properties of polygons in construction, industry, commerce, domestic, and artistic contexts.

Create and solve situational questions that involve the application of the properties of polygons.