1 of 8 0-day streak

Tests for similar triangles

Question 1 of 8

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Two triangles, \(PQR\) and \(XYZ\), are described below

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

In triangle \(PQR\), side \(PQ\) is 5 m; in triangle \(XYZ\), the corresponding side \(XY\) is 20 m

In triangle \(PQR\), side \(PR\) is 12 m; in triangle \(XYZ\), the corresponding side \(XZ\) is 48 m

In triangle \(PQR\), side \(QR\) is 13 m; in triangle \(XYZ\), the corresponding side \(YZ\) is 52 m

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

Complete the exact side-ratio checks for the proposed correspondence

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

(b)1 mark

Determine whether similarity is established and choose the valid reason

Similar: two side ratios alone are enough to apply SAS

Similar: \(\frac{XY}{PQ}=\frac{1}{4}\) is the second-to-first side ratio

Similar: all three corresponding side ratios are 4, so SSS applies

Similar: XY corresponds to PR, so their ratio gives the required correspondence

Similar: one side ratio \(\frac{XY}{PQ}=4\) is enough to prove similarity

State the scale factor \(k\) from the first triangle to the second. Give an exact fraction in lowest terms, or an integer

\(k\)

Format: exact fraction in lowest terms, or an integer