Question

complete the similarity statement and find the scale factor from the 1st figure to the 2nd figure.
△lkm ~ △square. scale factor (sf) = square (fraction)
△cbad ~ △square. sf = square (fraction)
△hjg ~ △square. sf = square (fraction)
△npm ~ △square. sf = square

Explanation:

Step1: Determine similar triangles for $\triangle NPM$

In the first set of triangles, $\triangle NPM$ and $\triangle RTV$ are similar. For the scale factor (SF), we use the ratio of corresponding sides. The sides of $\triangle NPM$ are \(6,8,10\) and the sides of $\triangle RTV$ are \(9,12,15\). The scale factor \(SF=\frac{6}{9}=\frac{2}{3}\) (using the shortest sides as the ratio of corresponding sides).

Step2: Determine similar triangles for $\triangle HJG$

For $\triangle HJG$ and $\triangle DTF$, the sides of $\triangle HJG$ are \(12,21,28\) and the sides of $\triangle DTF$ are \(9,15,18\). The scale factor \(SF = \frac{9}{12}=\frac{3}{4}\) (using the sides of the second - named triangle over the first - named triangle as per the problem's requirement of scale factor from the 1st figure to the 2nd figure).

Step3: Determine similar parallelograms for $\triangle CBAD$ (assuming it's a typo for parallelogram $ABCD$)

For parallelograms \(ABCD\) (with sides \(3,6,3,6\)) and \(WXYZ\) (with sides \(4,8,4,8\)), the scale factor \(SF=\frac{4}{3}\) (ratio of sides of \(WXYZ\) to \(ABCD\)).

Step4: Determine similar triangles for $\triangle LKM$

For $\triangle LKM$ (with sides \(6,9,12\)) and $\triangle SRO$ (assuming the correct notation, with sides \(4,6,8\)), the scale factor \(SF=\frac{4}{6}=\frac{2}{3}\) (ratio of sides of the second - named triangle to the first - named triangle).

Answer:

1. $\triangle NPM\sim\triangle RTV,SF = \frac{2}{3}$
2. $\triangle HJG\sim\triangle DTF,SF=\frac{3}{4}$
3. (Assuming parallelograms) If \(ABCD\sim WXYZ\), \(SF=\frac{4}{3}\)
4. $\triangle LKM\sim\triangle SRO,SF=\frac{2}{3}$