similartrianglesand solvingproblemsinvolvingthem.
ExploringSSS and SAS for SimilarTriangles
We’ll use geometrysoftwareand compass-and-straightedgeconstructionsto explorerelationshipsamong
trianglesbasedon proportionalside lengthsand congruentangles.
SSS for SimilarTriangles
Tech Note- GeometrySoftware
Use your geometrysoftwareto exploretriangleswithproportionalside lengths. Try this.1.
Set up two triangles, and , with eachside lengthof being timesthe
lengthof the correspondingside of.- Measuretheanglesof both triangles.
- Recordthe resultsin a chartlike the one below.
Repeatsteps1-3 for eachvalueof in the chart.Keep the samethroughoutthe exploration.TriangleData
- First,you knowthat all threeside lengthsin the two trianglesare proportional.That’s whatit meansfor
eachside in to be timesthe lengthof the correspondingside in.- You probablynoticewhathappenswith the anglemeasuresin. Eachtime you madea new
triangle for the givenvalueof , the measuresof , , and wereapproximately
the sameas the measuresof , , and. Like beforewhenwe experimentedwith the AA
and AAArelationships,thereis something“automatic”that happens.If thelengthsof the sidesof the
trianglesare proportional, that “automatically”makesthe anglesin the two trianglescongruenttoo. Of
course,oncewe knowthat the anglesare congruent,we also knowthat the trianglesare similarby AAA
or AA.
Hands-OnActivity
Materials:Ruler/straightedge,compass,protractor, graphor plainpaper.Directions:Work with a partnerin this activity. Eachpartnerwill use toolsto drawa triangle.Eachpartnercan work on a sheetof graphpaperor on plain paper. Makedrawingsas accurateas possible.
Notethat it doesn’tmatterwhatunit of lengthyou use.