When are two polygons similar? Use a square, a rhombus and a rectangle to show that one condition alone is not enough.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found. Given: a square, a rhombus and a rectangle. To show: each pair with the square fails one condition, so they are not similar.
2 · Draw the figure. Draw a square ABCD of side 3 cm, a rhombus PQRS of side 3 cm with ∠P = 60°, and a rectangle 3 cm by 5 cm. Mark the sides and angles.
3 · Write the formula or theorem. Two polygons with the same number of sides are similar if their corresponding angles are equal and their corresponding sides are in the same ratio.
4 · Square and rhombus. Sides: 3/3 = 1, so the ratio holds. Angles: ∠A = 90° but ∠P = 60°. The angles are not equal, so they are not similar.
5 · Square and rectangle. All angles are 90°. Sides: 3/3 = 1 but 3/5 ≠ 1. The sides are not in one ratio, so they are not similar.
6 · Check and box the answer. Both conditions must hold for polygons. One condition alone is not enough.
Scoring tip: Give one counter-example for each condition. Write the actual angles and side lengths so the examiner sees exactly which condition fails.
