L3 · Similarity clinic

Learning goal

“I can run the full similarity toolkit on mixed problems - angle sums of convex polygons, regular polygons, enlargements and reductions in both directions, and written justifications - and defend each verdict with both representations.”

Interior angle — the angle inside a convex polygon at one vertex; for n sides the interior angles always sum to (n - 2) x 180°.

Regular polygon — a convex polygon with all sides equal and all angles equal; any two regular polygons with the same number of sides are similar.

Reduction — a similar copy with scale factor less than 1 (the copy is smaller); enlargements have scale factor greater than 1.

Justification — a verdict plus the evidence: the matching angle list and the agreeing (or disagreeing) ratios, stated in words.

Worked example

Find the interior angle of a regular hexagon, then decide: is a regular hexagon with side 3 cm similar to one with side 7 cm? Step 1 (sum): (6 - 2) x 180° = 720° for any convex hexagon. Step 2 (regular -> equal shares): 720 / 6 = 120° per angle. Step 3 (verdict): both hexagons have all angles 120° (ANGLE list matches), and their sides give one ratio, 3/7 (RATIO table trivially agrees - every side of one is 3, every side of the other is 7). Similar - this is why ALL regular polygons with the same side-count are similar, whatever their size.

Check yourself — explain it

Any two regular octagons are similar because...

Paired problem — example still visible

Interior angle of a regular pentagon? -> 108° ((5 - 2) x 180 = 540; 540 / 5)

Faded completion — last step is yours

"A regular quadrilateral (a square) has angle sum ___ and each angle ___." -> 360°; 90°

Ready to practise?

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

Start practice →Take the unit quiz

Grade 10 — Mathematics 10-3 › T3U06 Similarity of Polygons

L3 · Similarity clinic