Triangles and Polygons
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Learning Objectives
- 1Identify polygons by counting sides and vertices
- 2Name common polygons including triangle, quadrilateral, pentagon, and hexagon
- 3Classify triangles by their sides as equilateral, isosceles, or scalene
- 4Classify triangles by their angles as right, acute, or obtuse
Mini Lesson
A polygon is a closed flat shape made only of straight line segments. Polygons are named by how many sides they have. The number of sides always matches the number of vertices (corners). Triangles are the simplest polygon family, and they get extra names based on their sides and their angles.
What Counts as a Polygon
- A polygon is closed — every side connects end-to-end with no gaps.
- Every side is a straight line segment — no curves.
- Sides only meet at the corners (vertices) — they do not cross.
- Circles, ovals, and any open figure are NOT polygons.
Naming Polygons by Side Count
- 3 sides — triangle.
- 4 sides — quadrilateral (square, rectangle, rhombus, trapezoid, and parallelogram all belong here).
- 5 sides — pentagon.
- 6 sides — hexagon.
- 7 sides — heptagon, 8 sides — octagon.
Triangles by Sides
- Equilateral triangle — all three sides are the same length, and all three angles are equal (60 degrees each).
- Isosceles triangle — exactly two sides are the same length, and the two angles opposite those sides are equal.
- Scalene triangle — all three sides are different lengths, so all three angles are different.
Triangles by Angles
- Right triangle — has exactly one 90-degree angle (a square corner).
- Acute triangle — every angle is less than 90 degrees.
- Obtuse triangle — has exactly one angle greater than 90 degrees.
- The three angles inside any triangle always add up to 180 degrees.
Tip: count sides to name a polygon, count equal sides to classify a triangle by sides, and check the largest angle to classify a triangle by angles.
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