Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence. In this case, you know the measur
e of two adjacent sides and the angle opposite to one of them. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. (Hint: Try constructing a triangle where the known angle is opposite to the shortest known side.) If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.
2 answers:
Answer with explanation:
SSA=Side-Side-Angle
Following are Congruency Criterion of two Triangles
(a)SSS (b)SAS (c)AAS or ASA or SAA are same. (d)RHS
If you Know two sides of triangle ,and one angle which is not in between these two angles, then the two Triangles can't be congruent.By using Sine rule , you can find remaining Angles and sides.
Consider two triangles ABC and DEF in which
----- AB=DE
-----BC=EF
----- ∠C=∠F
If you will use sine rule in these triangles ,you will get angle A and angle C different from angle D and angle E.
But, if the third side of two triangles are same then the two triangles will be congruent by SSS,SAS or ASA.
So, we can conclude that, SSA is not a valid criterion for congruency of Triangles.
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