Question

Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence. In this case, you know the measure 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.

Answer 1

To Find : Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence.

Solution:

Step 1 : Draw  a line segment AB

Step 2  :Draw an acute angle ( let say 45° ) at A  as AX

Step 3 : From B draw an altitude on AX     BY ⊥ AX

Step 4  Using suitable compass width and taking  Y as center cut AX  on both sides  at C and D

now BC = BD   as  BY is perpendicular bisector

Now compare ΔABC   and ΔABD

or instead of Step 3 and step 4 :

Using suitable compass width and taking B as center cut AX at 2 points C & D  directly  so BC = BD.

AB = AB    common

BC = BD     ( shown above)

∠A = ∠A     common

But ΔABC  s not congruent to ΔABD

as AC ≠ AD  

Hence SSA is not Valid  means for establishing triangle congruence.

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Answer 2

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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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