1 of 8 0-day streak

Tests for similar triangles

Question 1 of 8

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A triangles formed by two trees and their shadows is represented by triangles \(JKL\) and \(MNP\)

The proposed correspondence is \(J\leftrightarrow M\), \(K\leftrightarrow N\) and \(L\leftrightarrow P\)

In triangle \(JKL\), side \(JK\) is 3 m; in triangle \(MNP\), the corresponding side \(MN\) is 6 m

In triangle \(JKL\), side \(JL\) is 4 m; in triangle \(MNP\), the corresponding side \(MP\) is 8 m

In triangle \(JKL\), side \(KL\) is 5 m; in triangle \(MNP\), the corresponding side \(NP\) is 10 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

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

\(\frac{MN}{JK}=\square\) \(\frac{MP}{JL}=\square\) \(\frac{NP}{KL}=\square\)

(b)1 mark

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

Similar: two side ratios alone are enough to apply SAS

Similar: one side ratio \(\frac{MN}{JK}=2\) is enough to prove similarity

Similar: MN corresponds to JL, so their ratio gives the required correspondence

Similar: \(\frac{MN}{JK}=\frac{1}{2}\) is the second-to-first side ratio

Similar: all three corresponding side ratios are 2, so SSS applies

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