Triangle construction (SSS, SAS, ASA)

Task goals

• Identify which construction method (SSS, SAS, or ASA) applies given a rough sketch or a list of known measurements (three sides; two sides and the angle between them; two angles and the side between them).
• Construct a triangle from three given side lengths (SSS) by drawing the base to length, then striking two compass arcs (radii equal to the other two side lengths) from its endpoints to locate the third vertex.
• Construct a triangle from two given side lengths and the included angle (SAS) by drawing the two given sides at the given angle from a common vertex, then joining their free endpoints.
• Construct a triangle from two given angles and the included side (ASA) by drawing the given side to length, then drawing a ray at each given angle from its endpoints until they cross.
• Explain why each construction method produces a unique triangle (up to congruence) from the given measurements.