Distinguish the scale factor for side lengths from the scale factor for area.
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First lesson in this subject: Complete the angle sum
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Similar triangles have equal corresponding angles and proportional corresponding sides. If every side doubles, the new triangle has the same shape at twice the size in each direction.
A right triangle with legs 3 and 4 has area ½ × 3 × 4 = 6. Doubling both legs gives 6 and 8, so the area becomes ½ × 6 × 8 = 24. The area is four times as large, not twice.
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First lesson in this subject: Complete the angle sum
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Practice · Explore triangle inequalities, similar shapes and rhombus diagonals. Decide what follows from the givens.
Book · Explore measurements, transformations, coordinates and geometric relationships through diagrams and worked examples.
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