lesson
Use corresponding sides consistently
1 · Learn
Similar triangles have equal corresponding angles and corresponding side lengths in a common ratio. Match vertices before writing a proportion. Similarity preserves shape but need not preserve size.
One equal angle alone does not establish similarity. Two corresponding equal angles establish triangle similarity because the third angle then agrees too.
2 · Worked example
A side of 4 cm corresponds to 10 cm, giving factor 2.5 from small to large. A corresponding 6 cm side becomes 15 cm.
3 · Your turn
Similar triangles have corresponding sides 3 cm and 12 cm. What corresponds to 5 cm in the smaller triangle?
Check your answer
20 cm, using scale factor 4.
4 · Apply your learning
Use the supplied triangles ABC and DEF. Match A with D, B with E, and C with F. On plain paper construct a right triangle with perpendicular legs 4 cm and 6 cm, then one with legs 10 cm and 15 cm, using a ruler and set square. Compare with the supplied model. Check the displayed side ratios and explain why the hypotenuses have the same ratio; measuring is a check, not proof of similarity.
Adult guidance and safety
Require reasoning and a check. Provide accurate graphs, construction instruments and varied practice. Annual KS3 allocation is proposed; do not treat these short models as a complete assessed programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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