Scale factor lab

<p class="paragraph-header">Same shape, corresponding order</p>
<p>Similar figures have equal corresponding angles and one common ratio for corresponding lengths. Write \(\triangle ABC\sim\triangle PQR\) only when&nbsp;\(A\leftrightarrow P\), \(B\leftrightarrow Q\), \(C\leftrightarrow R\).</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">Test</th><th style="text-align: center; --cell-justify: center">Required corresponding information</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">AA</td><td style="text-align: center; --cell-justify: center">Two equal angle pairs; the third pair then follows.</td></tr><tr><td style="text-align: center; --cell-justify: center">SSS</td><td style="text-align: center; --cell-justify: center">Three pairs of sides in the same ratio.</td></tr><tr><td style="text-align: center; --cell-justify: center">SAS</td><td style="text-align: center; --cell-justify: center">Two pairs of sides in the same ratio and equal included angles.</td></tr></tbody></table></div></div>
<p>For&nbsp;\(\triangle ABC\sim\triangle PQR\), the scale factor from \(ABC\) to \(PQR\) is \(k=\dfrac{PQ}{AB}=\dfrac{QR}{BC}=\dfrac{PR}{AC}\). Reversing the direction gives&nbsp;\(\dfrac1k\). Congruent triangles are the special case \(k=1\).</p>
<p>With a line parallel to a triangle's side, name equal corresponding angles before using AA. Keep part-to-whole ratios consistent: if&nbsp;\(D\) lies between \(A\) and \(B\), then&nbsp;\(AB=AD+DB\).</p>

Similar figures have equal corresponding angles and one common ratio for corresponding lengths. Write \(\triangle ABC\sim\triangle PQR\) only when \(A\leftrightarrow P\), \(B\leftrightarrow Q\), \(C\leftrightarrow R\).

For \(\triangle ABC\sim\triangle PQR\), the scale factor from \(ABC\) to \(PQR\) is \(k=\dfrac{PQ}{AB}=\dfrac{QR}{BC}=\dfrac{PR}{AC}\). Reversing the direction gives \(\dfrac1k\). Congruent triangles are the special case \(k=1\).

With a line parallel to a triangle's side, name equal corresponding angles before using AA. Keep part-to-whole ratios consistent: if \(D\) lies between \(A\) and \(B\), then \(AB=AD+DB\).

Similarity tests and scale factors

Similarity tests and scale factors

Test	Required corresponding information
AA	Two equal angle pairs; the third pair then follows.
SSS	Three pairs of sides in the same ratio.
SAS	Two pairs of sides in the same ratio and equal included angles.