1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard VII
Mathematics
RHS Criteria for Congruency of Triangles
In the figure...
Question
In the figure,
P
Q
=
Q
R
=
R
S
=
S
P
. Then triangles are congruent by the postulate
A
SSS
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
SAS
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
ASA
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
All of these
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is
C
All of these
⇒
P
Q
=
O
R
=
R
S
=
S
P
[ Given ]
⇒
∠
S
P
R
=
∠
S
R
P
[ Base angles of equal sides also equal ]
⇒
∠
P
R
Q
=
∠
R
P
Q
[ Base angles of equal sides also equal ]
∴
∠
S
P
R
=
∠
S
R
P
=
∠
P
R
Q
=
∠
R
P
Q
(because geometry is a Rhombus)
In
△
P
R
S
and
△
P
R
Q
⇒
P
R
=
P
R
[ Common side ]
⇒
R
S
=
Q
R
[ Given ]
⇒
S
P
=
P
Q
[ Given ]
∴
△
P
R
S
≅
△
P
R
Q
[ By
S
S
S
congruence rule ]
Now,
⇒
S
R
=
P
Q
⇒
∠
S
R
P
=
∠
R
P
Q
[ From ( 1 ) ]
⇒
P
R
=
R
P
[ Common side ]
∴
△
P
R
S
≅
△
P
R
Q
[ By
S
A
S
congruence rule ]
Now,
⇒
∠
S
R
P
=
∠
R
P
Q
[ From ( 1 ) ]
⇒
P
R
=
R
P
[ Common side ]
⇒
∠
S
P
R
=
∠
P
R
Q
[ From ( 1 ) ]
∴
△
P
R
S
≅
△
P
R
Q
[ By
A
S
A
congruence rule ]
Suggest Corrections
0
Similar questions
Q.
In
△
A
B
C
a
n
d
△
P
Q
R
,
A
B
=
P
Q
,
A
C
=
P
R
a
n
d
B
C
=
Q
R
, then the two triangles are congruent by which test?
Q.
In triangles ABC and PQR, AB = PQ, BC = QR and CA = RP, then by which congruency criteria are these two triangles congruent?
Q.
In figure 5.15, In
□
PQRS the points A, B, C and D are the mid points of side PQ, side QR, side RS and side SP respectively.