CK12 - Geometry

1. Partner1: Drawa 6-8-10triangle.


2. Partner2: Drawa 9-12-15triangle.


3. Partner1: Measurethe anglesof your triangle.


4. Partner2: Measurethe anglesof your triangle.


5. Partners1 and 2: Compareyour results.

Whatdo you notice?

First,you knowthat all threeside lengthsin the two trianglesare proportional.

• You also probablynoticedthat the anglesin the two trianglesare congruent.You mightwantto repeat
  the activity, drawingtwo triangleswith proportionalside lengths.You shouldfind, again,that the angles
  in the trianglesare automaticallycongruent.


• Oncewe knowthat the anglesare congruent,then we knowthat the trianglesare similarby AAA or AA.

SSS for SimilarTriangles

Conclusion:If the lengthsof the sidesof two trianglesare proportional,then the trianglesare similar.This

is knownas SSS for similartriangles.

SAS for SimilarTriangles

SAS for SimilarTriangles

If the lengthsof two correspondingsidesof two trianglesare proportionaland the included

anglesare congruent,then the trianglesare similar.This is knownas SAS for similartri-

angles.

Example 1

Cherylmadethe diagrambelowto investigatesimilartrianglesmore.

She drew first, with , , and.

ThenCheryldid the following: