Question

introduction to similarity - item 32250
the two statements below are different ways to say that the sides of these similar triangles are proportional.
complete the equations that go with the statements.
image of two similar triangles, first with sides d, e, f; second with sides p, q, r
each pair of corresponding sides has the same ratio.
\\(\frac{d}{p} = \frac{\square}{q} = \frac{f}{\square}\\)

Explanation:

Step1: Identify corresponding sides

In similar triangles, corresponding sides are proportional. The first triangle has sides \(d\), \(e\), \(f\) and the second has \(p\), \(q\), \(r\). So \(d\) corresponds to \(p\), \(e\) corresponds to \(q\), and \(f\) corresponds to \(r\).

Step2: Fill in the proportions

For the first fraction \(\frac{d}{p}\), the second fraction should have \(e\) (corresponding to \(q\)) so \(\frac{e}{q}\), and the third fraction \(\frac{f}{r}\) (since \(f\) corresponds to \(r\)).

Answer:

\(\frac{d}{p} = \frac{e}{q} = \frac{f}{r}\)