Unit 4 · Core unit
Angle sums and the family tree of quadrilaterals, where each special case adds one property to the one above it.
What a strong answer looks like
A strong answer gives the most specific classification the evidence supports, and no more.
Know
Interior angles of an n-gon sum to 180 times two fewer than n. Exterior angles always sum to a full turn regardless of n.
Apply
Use the interior formula for one angle of a regular polygon by dividing by n.
Watch out
Applying the interior formula to an irregular polygon expecting equal angles.
Study move
Find one interior angle of a regular hexagon and one of a regular decagon.
Know
A parallelogram gains right angles to become a rectangle, equal sides to become a rhombus, and both to become a square.
Apply
Identify which additional property the evidence establishes, then name the most specific figure.
Watch out
Calling a rhombus a square because all sides are equal, which also requires right angles.
Study move
Given side lengths and slopes, classify a quadrilateral as specifically as the evidence allows.
Know
Distances, slopes, and midpoints computed from coordinates prove a classification without measurement.
Apply
Compute all four side lengths and the adjacent slopes before naming a figure.
Watch out
Concluding from a picture that looks square rather than from the computed slopes.
Study move
Prove a quadrilateral is a rhombus but not a square using coordinates.
Modeling drill
Given vertices at (0,0), (4,2), (6,6), and (2,4), classify the quadrilateral as specifically as the evidence allows.
