L2 · Vertices and angles of polygons: equal angles and right angles (by referent)

Learning goal

“I can count the vertices and angles of a polygon, and I can test an angle with the corner of a book or a piece of paper: if the corner fits exactly, the angle is a right angle. I can say whether a polygon's angles are all equal.”

Vertex — a corner of a polygon, where two sides meet. (More than one are called vertices.)

Angle — the opening at a vertex, between the two sides that meet there.

Right angle — an angle that matches the corner of a book or a piece of paper exactly. The capital letter L shows one.

Referent — a familiar object you compare against. The book corner is our referent for a right angle: we test angles against it instead of measuring.

Worked example

Count around a quadrilateral drawn on the board: side, corner, side, corner... It has 4 sides and 4 vertices, and at each vertex there is an angle - the opening between the two sides that meet there. Sides, vertices, and angles always come in the same count. Now test one angle: hold the corner of a piece of paper against it. The paper corner slides in with no gap and no overlap - it fits EXACTLY. That angle is a right angle. The paper corner is our referent: an angle is a right angle if the referent fits it exactly, a smaller angle if the opening is narrower than the corner, and a bigger angle if the opening is wider.

Check yourself — explain it

Why do we test with a book corner instead of just looking at the angle?

Paired problem — example still visible

How many vertices and how many angles does a hexagon have? -> 6 vertices and 6 angles

Faded completion — last step is yours

"An octagon has ___ vertices and ___ angles." -> 8; 8

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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