1908
You visited us
1908
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard VII
Mathematics
SAS Criteria for Congruency
In the given ...
Question
In the given figure, PA ⊥ AB, QB ⊥ AB and PA = QB.
Prove that ∆OAP ≅ ∆OBQ.
Is OA = OB?
Figure
Open in App
Solution
Given
:
P
A
⊥
A
B
Q
B
⊥
A
B
P
A
=
Q
B
To
prove
:
△
O
A
P
≅
△
O
B
Q
Find
whether
O
A
=
O
B
.
Proof
:
In
△
O
A
P
and
△
O
B
Q
:
∠
P
O
A
=
∠
Q
O
B
(
v
ertically
opposite
angles
)
∠
O
A
P
=
∠
O
B
Q
(
90
°
each
)
P
A
=
Q
B
(
g
iven
)
B
y
A
A
S
congruence
property
:
△
O
A
P
≅
△
O
B
Q
=
>
O
A
=
O
B
(
corresponding
parts
of
the
congruent
triangles
)
Suggest Corrections
0
Similar questions
Q.
Given figure,
P
A
⊥
A
B
,
Q
B
⊥
A
B
and
P
A
=
Q
B
, prove that
△
O
A
P
≅
O
B
Q
.
Q.
In the given figure, PA
⊥
AB, QB
⊥
AB and
△
OAP
≅
△
OBQ, then
Q.
In the adjoining figure, PA
⊥ AB, QB ⊥ AB and PA = QB. If PQ intersects AB at O, show that O is the midpoint of AB as well as that of PQ.