Do there exist two triangles, T1 and T2, such that
(a) they are not congruent, but
(b) for every side of T1, there is a side of T2 which has the same length and for every side of T2, there is a side of T1 which has the same length?
Justify your answer.
2007-01-30 11:47:56 · 6 answers · asked by cem_87 1 in Education & Reference ➔ Homework Help
No. The sss postulate says that if you have three congruent sides, then the triangles are congruent.
2007-01-30 11:53:23 · answer #1 · answered by Karen C 3 · 0⤊ 1⤋
Yes..T1 and T2 can be the same length but the angle between T1 and T2 in triangle 1 could be a different angle that the corresponding angle in triangle 2...therefore they would not be congruent
2007-01-30 19:53:51 · answer #2 · answered by angihorn2006 4 · 0⤊ 0⤋
I'd have to say no.
SSS
If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
SAS
If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
ASA
If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
AAS
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
HL
If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.
2007-01-30 19:55:02 · answer #3 · answered by lou53053 5 · 0⤊ 0⤋
Try drawing them and find out!
Seriously, if you know the length of all three sides of a triangle, do you not know all three angles as well?
Does not that set of data define one and only one triangle?
2007-01-30 20:02:02 · answer #4 · answered by Husker41 7 · 1⤊ 0⤋
I'll come back 2 you in 20 more years!
2007-01-30 19:52:06 · answer #5 · answered by Anonymous · 0⤊ 1⤋
I agree with him (the above)
2007-01-30 19:53:15 · answer #6 · answered by tswift 3 · 0⤊ 1⤋