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(2) Similarly, (ii) If ABAC, it can be proved

that‘ABC >‘ACB.

But this is also against the condition,

(3) So neither AB!AC nor ABAC

?AB AC (Proved)

Theorem 9 (SSS criterion)

If the three sides of one triangle are equal to the three corresponding sides of
another triangle, the triangles are congruent.

In 'ABCand'DEF,AB = DE,AC = DF

andBC=EF,

'ABC#'ABC.

Theorem 10 (ASA criterion)

If two angles and the included side of a triangle are equal to two corresponding
angles and the included side of another triangle, the triangles are congruent.

Let ABCandDEF be two triangles in which

the‘B=‘E,‘C =‘F. and the side BC

= the corresponding side EF, then the

triangles are congruent, i.e. 'ABC#'DEF.

Theorem 11 (HSA criterion)
If the hypotenuse and one side of a right-angled triangle are respectively equal
to the hypotenuse and one side of another right-angled triangle, the triangles
are congruent.

Let ABC and DEF be two right angled triangles, in which the hypotenuse AC=
hypotenuse DF and AB =DE, then 'ABC#'DEF..
Theorem 12

If one side of a triangle is greater than another, the angle opposite the greater
side is greater than the angle opposite the lesser sides.

Let ABC be a triangle whose AC >AB, then
‘ABC > ‘ACB.