Why doesn't SSA work for proving triangles congruent?

Question

PLease explain! but dont make it too confusing!

Answer 1

Hey there!

SSA stands for side-side-angle. In other words SSA means two sides and non-included angle of one triangle are congruent to two sides and non-included angle of another triangle, then the triangles are congruent.

This is false.

Let's take an example.

Let triangle ABC have sides AB=2, BC=3 and angle C=50 degrees.

Let triangle DEF have sides DE=2, EF=3 and angle D=50 degrees.

Well, we can use SSA. But corresponding parts of congruent triangles are not congruent. So SSA is false.

However, SSA can work in right triangles, a special case known as a HL (Hypotenuse-Leg) Congruence Theorem.

Overall, there's no such thing as SSA.

Likewise, if you spell SSA backwords, you get a curse word :).

SSA is false.

Hope it helps!

Answer 2

There can be multiple possibilities for the same triangle.
(ssa - side , side , angle) this angle must be non included.

Let s take this as an example:

let s say we have to construct a triangle abc with:
1. ab = 8cm
2.bc=7.3cm
3.angle a = 60^o
as we follow the ssa theorem

so we will first construct ab which 8cm
then angle a which is 60*(produce this to a good big length)
and keeping the compass needle on point b we will take 7.3cm as length.

now, this 7.3cm with compass must cut on the 60* to obtain bc as 7.3cm

As we can now see that this cuts on 60* at two points thus two such triangles with same measures can be possible.
this is why ssa is not considered as congruence of triangles theorem.

However it works with 90* and the theorem is called "RHS" namely: right (angle), hypotenuse(longest side) and side.(it works only and only with rhs theorem which is a special condition)

Answer 3

Ssa Theorem

Answer 4

ssa work proving triangles congruent

Answer 5

This Site Might Help You.

RE:
Why doesn't SSA work for proving triangles congruent?
PLease explain! but dont make it too confusing!

Answer 6

because it spells a bad word :-)

no, because there are actually two different triangles that can be formed using these specifications but for all other theorems, all triangles will always be congruent. This website has an applet to help explain how you can actually form 2 different triangles (usually one acute and one obtuse)

http://nlvm.usu.edu/en/nav/frames_asid_165_g_3_t_3.html?open=instructions

Answer 7

because it is possible to draw two different triangles
which has two congruent sides and one angle yet completely different angles because the two other angles are not the same.

I can't draw it here, but you must be able to find the figure in your math book for this.

Answer 8

Side Side Angle Theorem