Lesson 4.1
Polygon Angle Sums
A diagonal fan divides a convex polygon with n sides into n minus two triangles. The exterior angles, taking one consistent turn at each vertex, total a full revolution.
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Unit 4
Polygons and Quadrilaterals
Angle sums and the family tree of quadrilaterals, where each special case adds one property to the one above it.
Lessons and exercises
Lesson 4.2
The Quadrilateral Family
A parallelogram has two pairs of parallel opposite sides. Rectangles add right angles, rhombi add four equal sides, and squares satisfy both conditions. Definitions are inclusive: every square is a rectangle and a rhombus.
Lesson 4.3
Coordinate Proofs
Coordinates turn geometric claims into calculations involving slope, distance, and midpoint. Choose coordinates that simplify the figure without imposing extra conditions. Horizontal and vertical lines require separate treatment when a slope is undefined.
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