Mathematics Class 9
4-gons (Quadrilaterals)
Prove what forces the parallelogram name, and tile a floor with any four-sided shape.
14 lessons · ~111 min total
Track progress — 0 of 14 lessons read 0%
Lessons in this topic
- 0 Start here A roadmap: which measurements force the parallelogram name, the midpoint theorem, the centroid, the midpoint 4-gon, symmetry and tiling. · 4 min You are here
- 1 Which claims force the name A property starts from the name. A test must earn the name from a measurement, and not every measurement can. · 8 min
- 2 One diagonal, two triangles If triangle ABC lands exactly on triangle CDA, both pairs of opposite sides of ABCD are parallel. · 9 min
- 3 Both pairs equal prove it If both pairs of opposite sides are equal, the shape is a parallelogram. One diagonal and SSS prove it. · 9 min
- 4 Three more ways in One pair equal and parallel, diagonals that bisect each other, and opposite angles equal: three more routes to the name. · 9 min
- 5 The midpoint theorem A segment joining two side midpoints of a triangle is parallel to the third side and exactly half of it. · 9 min
- 6 Checkpoint: earning the name A graded check on the first five ideas. · 6 min
- 7 Three medians, one point The three medians of a triangle meet at the centroid, which splits each one 2 to 1 from the corner. · 9 min
- 8 Four halfway points, one parallelogram Join the side midpoints of any quadrilateral, in order, and the inner shape is always a parallelogram. · 10 min
- 9 Fold lines and half-turns A square folds four ways. A parallelogram has no fold line but turns onto itself after a half-turn. · 8 min
- 10 Any four-gon covers a floor Four copies of any quadrilateral, one corner from each, fill a meeting point exactly. So any four-sided tile covers a floor. · 9 min
- 11 Checkpoint: midpoints, symmetry and tiles A graded check on the centroid, the midpoint 4-gon, fold lines and half-turns, and tiling. · 6 min
- 12 The big picture Nine ideas on one screen, each a claim about four corners and the argument that earned it. · 6 min
- 13 Track quiz A cheat-sheet table plus a reveal quiz, one question for each idea. · 9 min
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