Congruent Sides of Triangles

[dubs84]

I know this is a silly question but it does not state that this is true, or talk about it anywhere, in the geometry book that I am using. If you are given two triangles and you do not know that they are congruent, if you know that two of the sets of corresponding sides are congruent, then must the third set of corresponding sides be congruent?





For instance in the diagram above, since two sets of corresponding sides are congruent and it is a closed figure triangle, mustn't the third set of corresponding sides be congruent?

 

[jashan1985]

I know this is a silly question but it does not state that this is true, or talk about it anywhere, in the geometry book that I am using. If you are given two triangles and you do not know that they are congruent, if you know that two of the sets of corresponding sides are congruent, then must the third set of corresponding sides be congruent?


View attachment 3069


For instance in the diagram above, since two sets of corresponding sides are congruent and it is a closed figure triangle, mustn't the third set of corresponding sides be congruent?

As far as I understand what you are asking here. I would like to say that having pair of sides equal in 2 different triangles, does not mean that angles between those sides are also equal.

Lets take an example.

In triangle ABC and PRQ.

We have AC=PQ and AB=PR, but angle BAC is not equal to RPQ. And, also the third side BC is not equal to QR.

 

[Deleted member 4993]

I know this is a silly question but it does not state that this is true, or talk about it anywhere, in the geometry book that I am using. If you are given two triangles and you do not know that they are congruent, if you know that two of the sets of corresponding sides are congruent, then must the third set of corresponding sides be congruent?


View attachment 3069


For instance in the diagram above, since two sets of corresponding sides are congruent and it is a closed figure triangle, mustn't the third set of corresponding sides be congruent?

If triangles ABC and A'B'C' are congruent - then it means that corresponding sides are equal and corresponding angles are equal. Thus:

CA = C'A' ; A'B' = AB ; B'C' = BC and mBCA = mB'C'A' ; mABC = mA'B'C' ; mCAB = mC'A'B'

In other words,

if you lift the triangle A'B'C' and place it on ABC such that point A coincides point A' and line AB coincides with line A'B'

then

point B' will coincide with point B and point C' will coincide with point C.

 

[HallsofIvy]

I suggest you read your geometry book more closely. Every geometry book I have ever seen dealt with "side-angle-side" congruence of triangles which is what you are talking about here.

 

[Deleted member 4993]

You pay for a $35 purchase this way:
3 bills: $5, $10, $20
or
3 bills: $10, $5, $20

Is there a difference?

But that does not make a triangle because 10+5 < 20 (triangle inequality fails!)