1 of 8 0-day streak

Tests for similar triangles

Question 1 of 8

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Two triangles, \(ABC\) and \(DEF\), are described below

The proposed correspondence is \(A\leftrightarrow D\), \(B\leftrightarrow E\) and \(C\leftrightarrow F\)

In triangle \(ABC\), side \(AB\) is 6 cm; in triangle \(DEF\), the corresponding side \(DE\) is 18 cm

In triangle \(ABC\), side \(AC\) is 8 cm; in triangle \(DEF\), the corresponding side \(DF\) is 24 cm

In triangle \(ABC\), side \(BC\) is 10 cm; in triangle \(DEF\), the corresponding side \(EF\) is 27 cm

Decide similarity using this proposed correspondence. Do not change the vertex matching

Figures use separate drawing scales. Compare the stated corresponding dimensions, not their displayed sizes

(a)3 marks

Find each available image-to-original side ratio before deciding on similarity

\(\frac{DE}{AB}=\square\) \(\frac{DF}{AC}=\square\) \(\frac{EF}{BC}=\square\)

(b)1 mark

Decide whether the stated data establishes that the triangles are similar. Select the complete verdict and reason

Not similar: DE corresponds to AC, so their ratio gives the required correspondence

Similar: one side ratio \(\frac{DE}{AB}=3\) is enough to prove similarity

Not similar: two side ratios alone are enough to apply SAS

Not similar: \(\frac{DE}{AB}=\frac{1}{3}\) is the second-to-first side ratio

Not similar: the first two ratios are 3, but the third is \(\frac{27}{10}\)