Two triangles are necessarily congruent if and only if __________.?

Answer 1

if they have--
all sides equal(sss)
two sides n included angle equal(sas)
two angles n included side equal(asa)

in right triang. if hypotn n any other sides r equal. (same as sas

Answer 2

One of three conditions apply:

SSS: all three sides are equal
SAS: two sides and the included angle are equal
ASA: two angles and the included side are equal

Not necessarily congruent:

SSA allows the possibility of two distinct triangles
AAA means the triangles are similar, but without a size item (the length of a side), congruency is not guaranteed.

Answer 3

two triangles are congruent if, and only if, they have 3 pairs
of congruent sides and three pairs of congruent angles. In other words, triangle ABC and triangle XYZ are congruent if, and only if, angle A is congruent to angle X, angle B is congruent to
angle Y, angle C is congruent to angle Z, side XY is congruent to side AB, side BC is congruent to side YZ, and side AC is congruent to side XZ.

Note that when you say two triangles are congruent, you have to get the letters in the proper order to show what's congruent to what. If I had said triangle BAC was congruent to triangle YXZ,
then that's okay (check it out). But if I say that triangle YZX
is congruent to triangle CAB, then that's wrong.

Answer 4

There are several ways to prove two triangles congruent.
*side-side-side (all 3 sides congruent-SSS)
*side-angle-side (2 sides and included angle congruent-SAS)
*angle-side-angle (2 angles and included side congruent-ASA)
*angle-angle-side (2 angles and opposite side congruent-AAS)
*hypotenuse-leg (leg and hypotenuse congruent of two right triangles-HL)

There probably other ways to do so, but these are the most commonly used methods.

NOTE: These are the ways that can't prove two triangles congruent.

*side-side-angle (2 sides and opposite angle congruent-SSA)
*angle-angle-angle (all 3 angles congruent-AAA...this can prove similarity though)

Answer 5

If the sides are corresponding

Answer 6

Their corresponding sides have equals lengths.

Use "iff". It saves space.

Answer 7

yes corrsponding sides

Answer 8

This puzzles me too

Answer 9

I think it depends