Scale factor lab

<p>Similar triangles have equal corresponding angles and proportional corresponding sides.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--3" data-layout="3"><div class="question-column" style="flex: 1; align-self: flex-start;"><p class="paragraph-header" style="text-align: center">AA similarity</p><div class="graph-block" data-graph-config="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" data-width="155" data-height="100" data-proportional style="width:155px;height:100px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:155px;--graph-aspect:155 / 100;"></div></div><div class="question-column" style="flex: 1; align-self: flex-start;"><p class="paragraph-header" style="text-align: center">SSS similarity</p><div class="graph-block" data-graph-config="eyJheGlzIjpmYWxzZSwiZ3JpZCI6ZmFsc2UsIndpZHRoIjoxNTUsImhlaWdodCI6MTAwLCJlbGVtZW50cyI6W3siaWQiOiJtYXRoLWF1ZGl0LXNpbS1TU1MtMSIsInR5cGUiOiJwb2x5Z29uIiwiY29sb3IiOiIjMDAwMDAwIiwicG9pbnRzIjpbWzAuOCwxLjZdLFswLDBdLFsyLDBdXSwiZmlsbENvbG9yIjoibm9uZSIsImZpbGxPcGFjaXR5IjowLCJzdHJva2VXaWR0aCI6MS41fSx7IngiOjAuOCwieSI6MS45MjAwMDAwMDAwMDAwMDAyLCJpZCI6Im1hdGgtYXVkaXQtc2ltLVNTUy0yIiwidHlwZSI6InRleHQiLCJjb2xvciI6IiMwMDAwMDAiLCJsYWJlbCI6IlxcKEFcXCkiLCJ0ZXh0QW5jaG9yWCI6Im1pZGRsZSJ9LHsieCI6MCwieSI6LTAuNCwiaWQiOiJtYXRoLWF1ZGl0LXNpbS1TU1MtMyIsInR5cGUiOiJ0ZXh0IiwiY29sb3IiOiIjMDAwMDAwIiwibGFiZWwiOiJcXChCXFwpIiwidGV4dEFuY2hvclgiOiJtaWRkbGUifSx7IngiOjIsInkiOi0wLjQsImlkIjoibWF0aC1hdWRpdC1zaW0tU1NTLTQiLCJ0eXBlIjoidGV4dCIsImNvbG9yIjoiIzAwMDAwMCIsImxhYmVsIjoiXFwoQ1xcKSIsInRleHRBbmNob3JYIjoibWlkZGxlIn0seyJpZCI6Im1hdGgtYXVkaXQtc2ltLVNTUy01IiwidHlwZSI6InBvbHlnb24iLCJjb2xvciI6IiMwMDAwMDAiLCJwb2ludHMiOltbNSwyLjQwMDAwMDAwMDAwMDAwMDRdLFszLjgsMF0sWzYuOCwwXV0sImZpbGxDb2xvciI6Im5vbmUiLCJmaWxsT3BhY2l0eSI6MCwic3Ryb2tlV2lkdGgiOjEuNX0seyJ4Ijo1LCJ5IjoyLjcyLCJpZCI6Im1hdGgtYXVkaXQtc2ltLVNTUy02IiwidHlwZSI6InRleHQiLCJjb2xvciI6IiMwMDAwMDAiLCJsYWJlbCI6IlxcKFhcXCkiLCJ0ZXh0QW5jaG9yWCI6Im1pZGRsZSJ9LHsieCI6My44LCJ5IjotMC40LCJpZCI6Im1hdGgtYXVkaXQtc2ltLVNTUy03IiwidHlwZSI6InRleHQiLCJjb2xvciI6IiMwMDAwMDAiLCJsYWJlbCI6IlxcKFlcXCkiLCJ0ZXh0QW5jaG9yWCI6Im1pZGRsZSJ9LHsieCI6Ni44LCJ5IjotMC40LCJpZCI6Im1hdGgtYXVkaXQtc2ltLVNTUy04IiwidHlwZSI6InRleHQiLCJjb2xvciI6IiMwMDAwMDAiLCJsYWJlbCI6IlxcKFpcXCkiLCJ0ZXh0QW5jaG9yWCI6Im1pZGRsZSJ9XSwiYWxpZ25tZW50IjoiY2VudGVyIiwic2hvd1hBeGlzIjpmYWxzZSwic2hvd1lBeGlzIjpmYWxzZSwiYm91bmRpbmdCb3giOlstMC41LDMuMzUsNy4zLC0xLjY4MjI1ODA2NDVdLCJzaG93QXhpc0xhYmVscyI6ZmFsc2UsInNob3dOYXZpZ2F0aW9uIjpmYWxzZSwia2VlcEFzcGVjdFJhdGlvIjp0cnVlfQ==" data-width="155" data-height="100" data-proportional style="width:155px;height:100px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:155px;--graph-aspect:155 / 100;"></div></div><div class="question-column" style="flex: 1; align-self: flex-start;"><p class="paragraph-header" style="text-align: center">SAS similarity</p><div class="graph-block" data-graph-config="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" data-width="155" data-height="100" data-proportional style="width:155px;height:100px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:155px;--graph-aspect:155 / 100;"></div></div></div></div>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 490px;"><colgroup><col style="width: 30.6122%;"><col style="width: 69.3878%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Test</strong></th><th style="text-align: center; --cell-justify: center"><strong>What must match</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">AA similarity</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">SSS similarity</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">SAS similarity</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr></tbody></table></div></div>
<p>If&nbsp;\(\triangle ABC\sim\triangle XYZ\), then&nbsp;\(\dfrac{XY}{AB}=\dfrac{YZ}{BC}=\dfrac{XZ}{AC}\). Keep corresponding vertices in the same order.</p>

Similar triangles have equal corresponding angles and proportional corresponding sides.

\(\begin{aligned} \angle BAC&=\angle YXZ \\ \angle ABC&=\angle XYZ \end{aligned}\)

\(\dfrac{XY}{AB}=\dfrac{YZ}{BC}=\dfrac{XZ}{AC}\)

\(\dfrac{XY}{AB}=\dfrac{XZ}{AC}\)
\(\angle BAC=\angle YXZ\) (included angle)

If \(\triangle ABC\sim\triangle XYZ\), then \(\dfrac{XY}{AB}=\dfrac{YZ}{BC}=\dfrac{XZ}{AC}\). Keep corresponding vertices in the same order.

Similarity Tests

Similarity Tests

Video Solution:

Solution:

Solution locked

Test	What must match
AA similarity
SSS similarity
SAS similarity