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: Identify similar triangles for $\triangle NPM$

For $\triangle NPM$, the similar triangle is $\triangle LKJ$.
The sides of $\triangle NPM$ are \(6,8,10\) and the sides of $\triangle LKJ$ are \(9,12,15\).
The scale factor \(SF=\frac{9}{6}=\frac{3}{2}\)

Step2: Identify similar triangles for $\triangle HJG$

For $\triangle HJG$, the similar triangle is $\triangle DTF$.
The sides of $\triangle HJG$ are \(12,24,24\) and the sides of $\triangle DTF$ are \(9,18,18\).
The scale factor \(SF = \frac{9}{12}=\frac{3}{4}\)

Step3: Identify similar parallelograms for $\parallelogram CBAD$

For $\parallelogram CBAD$, the similar parallelogram is $\parallelogram WXYZ$.
The sides of $\parallelogram CBAD$ are \(3,6,3,6\) and the sides of $\parallelogram WXYZ$ are \(4,8,4,8\).
The scale factor \(SF=\frac{4}{3}\)

Step4: Identify similar triangles for $\triangle LKM$

For $\triangle LKM$, the similar triangle is $\triangle SOH$.
The sides of $\triangle LKM$ are \(9,12,6\) and the sides of $\triangle SOH$ are \(6,8,4\).
The scale factor \(SF=\frac{6}{9}=\frac{2}{3}\)

Answer:

1. $\triangle NPM\sim\triangle LKJ$, $SF = \frac{3}{2}$
2. $\triangle HJG\sim\triangle DTF$, $SF=\frac{3}{4}$
3. $\parallelogram CBAD\sim\parallelogram WXYZ$, $SF=\frac{4}{3}$
4. $\triangle LKM\sim\triangle SOH$, $SF=\frac{2}{3}$