1 of 8 0-day streak

Tests for similar triangles

Question 1 of 8

Calculator allowed

Consider triangles \(PQR\) and \(XYZ\) using the stated measurements

The proposed correspondence is \(P\leftrightarrow X\), \(Q\leftrightarrow Y\) and \(R\leftrightarrow Z\)

In triangle \(PQR\), side \(PQ\) is 9 cm; in triangle \(XYZ\), the corresponding side \(XY\) is 27 cm

In triangle \(PQR\), side \(PR\) is 12 cm; in triangle \(XYZ\), the corresponding side \(XZ\) is 36 cm

In triangle \(PQR\), side \(QR\) is 15 cm; in triangle \(XYZ\), the corresponding side \(YZ\) is 40 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

Compare the stated corresponding sides by forming second triangle ÷ first triangle

\(\frac{XY}{PQ}=\square\) \(\frac{XZ}{PR}=\square\) \(\frac{YZ}{QR}=\square\)

(b)1 mark

Select the statement that applies the relevant similarity test correctly

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

Not similar: XY corresponds to PR, so their ratio gives the required correspondence

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

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

Not similar: the first two ratios are 3, but the third is \(\frac{8}{3}\)