SSS Criteria

Move points A, B and C to change the shape of the triangles. Click on triangle ABC to move the triangles. Use the toolbar to measure line segments, angle measures and area.

Question 1

Since we are given no information about the angles, to prove congruence we cannot simply reflect across AB. We begin by drawing an auxiliary line from B to E. Click on auxiliary line and isosceles triangles.[br][br]This auxiliary line creates what two triangles?

ABE CBE DEF ABC

Question 2

Select auxiliary angles. What are you noticing about the base angles of the blue triangle ABE and the base angles of the orange triangle CBE? What kind of triangles are ABE and CBE?

Question 3

Which of the following is true, if ABE and CBE are isosceles triangles with congruent base angles?

triangle ABC = triangle DEF by ASA angle ABC = angle DEF angle BAE = angle BCE triangle ABC = triangle DEF by SAS

Question 4

Explain why ASA triangle congruence is an extension of SAS?