CONGRUENCE OF TRIANGLES
Let AAGC and APQR be two congruent triangles. Super-pose AABC on APOR
it exactly. In such a super-position, the vertices of AABC will fall on the vertices of APOR
order. Suppose, vertex A falls on vertex P. vertex B falls on vertex Q, and vertex C tells
R. then side AB will fall on side PQ, BC on QR and CA on RP. Also A will super-pos
corresponding angle P, 28 on 2Q and AC on ZR.
the sides and angles of the two triangles. And if the super-position is exact, i.e. the tria
The order in which the vertices match, determines a matching or correspondence
congruent, then the corresponding sides and angles are congruent. Thus, we have six
In the above discussion, we have considered one correspondence between the v
triangles ABC and PQR which was ABC HPQR, i.e. A HP, B Q and C <> R. But,
be many other matchings possible between the vertices of two triangles, and the triangl
may not be congruent under all these matchings. If we have two triangles ABC and PQA
three of corresponding sides and three of corresponding angles. That is:
(corresponding anglesa
Two triangles are congruent, if pairs of corresponding sides and correspo
A(P)
4
B (Q)
Fig. 9.4
(corresponding sides
CA = RP
AB = PQ,
BC = QR
c
A = P
B = 2Q, ZC = ZR
angles are congruent.
following six matchings are possible:
APBQ and C R written as ABC HPQR
A HQ, BAR and C P written as ABC HQRP
A R BA P and C H Q written as ABC RPQ
A HP, B Rand C H Q written as ABC + PRQ
AQ, BAP and C o R written as ABC QPR
A HR, BAQ and CP written as ABC HRQP
166
Answers
Answer:
CONGRUENCE OF TRIANGLES
Let AAGC and APQR be two congruent triangles. Super-pose AABC on APOR
it exactly. In such a super-position, the vertices of AABC will fall on the vertices of APOR
order. Suppose, vertex A falls on vertex P. vertex B falls on vertex Q, and vertex C tells
R. then side AB will fall on side PQ, BC on QR and CA on RP. Also A will super-pos
corresponding angle P, 28 on 2Q and AC on ZR.
the sides and angles of the two triangles. And if the super-position is exact, i.e. the tria
The order in which the vertices match, determines a matching or correspondence
congruent, then the corresponding sides and angles are congruent. Thus, we have six
In the above discussion, we have considered one correspondence between the v
triangles ABC and PQR which was ABC HPQR, i.e. A HP, B Q and C <> R. But,
be many other matchings possible between the vertices of two triangles, and the triangl
may not be congruent under all these matchings. If we have two triangles ABC and PQA
three of corresponding sides and three of corresponding angles. That is:
(corresponding anglesa
Two triangles are congruent, if pairs of corresponding sides and correspo
A(P)
4
B (Q)
Fig. 9.4
(corresponding sides
CA = RP
AB = PQ,
BC = QR
c
A = P
B = 2Q, ZC = ZR
angles are congruent.
following six matchings are possible:
APBQ and C R written as ABC HPQR
A HQ, BAR and C P written as ABC HQRP
A R BA P and C H Q written as ABC RPQ
A HP, B Rand C H Q written as ABC + PRQ
AQ, BAP and C o R written as ABC QPR
A HR, BAQ and CP written as ABC HRQP
166
Step-by-step explanation:
CONGRUENCE OF TRIANGLES
Let AAGC and APQR be two congruent triangles. Super-pose AABC on APOR
it exactly. In such a super-position, the vertices of AABC will fall on the vertices of APOR
order. Suppose, vertex A falls on vertex P. vertex B falls on vertex Q, and vertex C tells
R. then side AB will fall on side PQ, BC on QR and CA on RP. Also A will super-pos
corresponding angle P, 28 on 2Q and AC on ZR.
the sides and angles of the two triangles. And if the super-position is exact, i.e. the tria
The order in which the vertices match, determines a matching or correspondence
congruent, then the corresponding sides and angles are congruent. Thus, we have six
In the above discussion, we have considered one correspondence between the v
triangles ABC and PQR which was ABC HPQR, i.e. A HP, B Q and C <> R. But,
be many other matchings possible between the vertices of two triangles, and the triangl
may not be congruent under all these matchings. If we have two triangles ABC and PQA
three of corresponding sides and three of corresponding angles. That is:
(corresponding anglesa
Two triangles are congruent, if pairs of corresponding sides and correspo
A(P)
4
B (Q)
Fig. 9.4
(corresponding sides
CA = RP
AB = PQ,
BC = QR
c
A = P
B = 2Q, ZC = ZR
angles are congruent.
following six matchings are possible:
APBQ and C R written as ABC HPQR
A HQ, BAR and C P written as ABC HQRP
A R BA P and C H Q written as ABC RPQ
A HP, B Rand C H Q written as ABC + PRQ
AQ, BAP and C o R written as ABC QPR
A HR, BAQ and CP written as ABC HRQP
166