Corollaries of Similar Triangles (Leaving Cert Mathematics): Flashcards

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Corollaries of Similar Triangles
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Line divides 2 sides proportionally → relation to 3rd side?

Parallel to the third side

What does proportional division create in a triangle?

Similar triangles

Corollary 6: Area ratio in similar triangles equals?

Square of the ratio of corresponding sides

Formula: Area ratio for similar triangles

A1A2=(s1s2)2\frac{A_1}{A_2} = \left(\frac{s_1}{s_2}\right)^2

What's proportional in similar triangles besides sides?

Heights

How areas scale with side ratios (similar triangles)

Quadratically

If ADDB=AEEC\frac{AD}{DB} = \frac{AE}{EC}, then DEDE & BCBC are?

Parallel

Similar triangles: side ratio 69\frac{6}{9}, area ratio?

49\frac{4}{9} (square the simplified ratio)

Corollary 5 in brief

Proportional division → parallel to 3rd side

Why is area ratio = (side ratio)² in similar triangles?

Area depends on base & height, both proportional

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