Consider this two triangles in the above diagrams
To determine if two triangles are indeed congruence,we must look at its sides and it angles.
AB=DE,
BC=EF,
Next,if we need to prove that two triangles are congruent, we have five different methods:
SSS (side side side) =
If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
SAS (side angle side) =
ASA (angle side angle) =
If two angles and the side in between are congruent to the corresponding parts of another triangle, the triangles are congruent.
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
RHS (Right-angle hypotenuse side) =
If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent. Remember that if we know two sides of a right triangle we know the third side anyway, so this is really just SSS.In addition,to find the side of any triangles,we have to apply the pythagoras theorem.
NOTE 1: AAA works fine to show that triangles are the same SHAPE (similar), but does NOT work to show congruence. You can draw 2 equilateral triangles that are the same shape but not the same size.
NOTE 2: The Angle Side Side Theorem (yes, we all know what it spells) does NOT necessarily work.
For example,
Is triangle ABC congruent to triangle DEF?
In the pictures we have:
angle A = angle D.
angle B = angle E.
side AC = side DF.
That's congruency! (:
