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Side-Angle-Side: Quick Investigation

Interact with this app below for a few minutes. Be sure to move each slider to see what it does. Be sure to also move the LARGE POINTS (vertices) of these triangles.

In the app above, what do you notice? What do you wonder?

Make a conjecture about the two triangles you see above.

In the app below here, use any one (or more) of the GeoGebra tools to informally prove your conjecture is true.

Suppose two sides of one triangle are drawn in proportion to two sides of another triangle, and suppose their included angles are also congruent. What can we conclude about these two triangles? Why can we conclude this?