Lesson 2 · Triangle, Quadrilateral and Polygon

Polygons Presentation

MathematicsSubject
14 minEstimated read
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Unit 2 · Triangle, Quadrilateral and Polygon

Polygons

Mathematics · Grade 7

What You Will Be Able To Do

✂️

Find the angle sum of any polygon by cutting it into triangles

🔢

Use (n - 2) x 180 and explain where every part of it comes from

⭐

Say what makes a polygon regular, and find one of its angles

🔄

Use the fact that exterior angles always total 360°, whatever the shape

Cut It Into Triangles

1Pick any one corner of the polygon
2Join it to every corner it is not already joined to by a side
3You cannot reach yourself or your two neighbours, so that is n - 3 diagonals
4Each diagonal adds one piece, so you finish with n - 2 triangles
5Every triangle gives 180°, so the total is (n - 2) x 180

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Presenter notes: Start by asking the class for the angle sum of a triangle, then a quadrilateral, both of which they know. Then ask for a shape with twenty sides and watch the room go quiet. Tell them nobody is going to measure anything and nobody is going to memorise a new fact, because the answer comes from a trick they used last lesson. That framing matters: this topic looks like it needs a formula sheet and it actually needs one idea used repeatedly.