Find the sum of the interior angles of a 5-gon.
Unit 07 · Lesson 07 · Polygons & Quadrilaterals
Polygon Decomposition & Design Constraints
Classify polygons and quadrilaterals using angle sums, side relationships, diagonals, symmetry, and coordinate evidence.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to classify polygons and quadrilaterals using angle sums, side relationships, diagonals, symmetry, and coordinate evidence.
Success evidence
- Label the figure and units before calculating.
- Select and justify the governing definition, theorem, relationship, or construction.
- Show enough work that another learner can audit the conclusion.
- Check the result against the diagram, scale, and stated constraints.
Visual model
Classify polygons and quadrilaterals using angle sums, side relationships, diagonals, symmetry, and coordinate evidence.
S=(n-2)180^\circE=360^\circA=\frac12 aP
Worked reasoning
Process: List the properties required by the classification, calculate or prove each one, then state the most specific valid name.
- Read the figure and rewrite all given information with correct notation.
- Identify the exact relationship that connects the known and unknown quantities.
- Substitute, construct, or prove one justified step at a time.
- State the result with units and a sentence explaining what it means.
Misconception check: A square belongs to both the rectangle and rhombus families; classifications are hierarchical rather than mutually exclusive.
Khaemenes Academy · Open-Age Geometry
Polygon Decomposition & Design Constraints
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
Find each exterior angle of a regular 5-gon.
Which quadrilateral has four congruent sides and four right angles?
What do the diagonals of a parallelogram do?
What additional property turns a parallelogram into a rectangle?
A regular polygon has perimeter 48 and apothem 7. Find its area.