Download Congruence of triangles

Congruence of triangles
Two triangles are said to be congruent, if all the corresponding parts are equal.
The symbol used for denoting congruence is  and  PQR  STU implies
that
and also
i.e. corresponding angles and corresponding sides are equal.
In order to prove that two triangles are congruent, it is not always necessary to
show that all the six corresponding parts are equal. If certain basic requirements
are met the triangles are said to be congruent. These basic criteria are
embodied in the five postulates given below.
SSS Postulate
If all the sides of one triangle are congruent to the corresponding sides of
another triangle then the triangles are congruent.
seg. AB = seg. PQ , seg. BC = seg. QR and
seg. CA = seg. RP
 ABC  PQR by S S S.
SAS Postulate
If the two sides and the angle included in one triangle are congruent to the
corresponding two sides and the angle included in another triangle then the two
triangles are congruent (figure 2.16).
seg. AB = seg. PQ , seg. BC = seg. QR and
m  ABC = m  PQR
 ABC  PQR by S A S postulate.
ASA Postulate
If two angles of one triangle and the side they include are congruent to the
corresponding angles and side of another triangle the two triangles are
congruent (figure 2.17 ).
Figure 2.17
m  B + m  R m  L = m  P and seg. BC = seg. RP
 ABC  QRP by A S A postulate.
AAS Postulate
If two angles of a triangle and a side not included by them are congruent to the
corresponding angles and side of another triangle the two triangles are
congruent (figure 2.18)
Figure 2.18
m A = m P, m B = m Q, and AC = PR
 ABC  PQR by A A S.
HL Postulate
This postulate is applicable only to right triangles. If the hypotenuse and any
one leg of a right triangle are congruent to the hypotenuse and the
corresponding side of another right triangle then the two triangles are congruent
Then hypotenuse AC = hypotenuse PR
Leg AB = Side PQ
  ABC   PQR by H: postulate.