the given figure show a parallelogram ABCD . Squares ABPQ and ADRS are drawn on sides AB and AD of the parallelgram . Show that angle SAQ is equal to Angle ABC.
Answers
In quadrilateral A B C D
, we have A B = C D and A D = B C
Now join segment A C
Now in
Δ
A
B
C
and
Δ
A
C
D
, we have
A
B
=
C
D
---------------- already given
A
D
=
B
C
---------------- already given
and
A
C
=
A
C
---------------- common
Hence
Δ
A
B
C
≡
Δ
A
C
D
∴
∠
D
A
C
=
∠
B
C
A
- both opposite equal sides
D
C
and
A
B
, and
∴
C
D
||
A
B
- as alternate angles are equal
∴
∠
D
C
A
=
∠
C
A
B
- both opposite equal sides
A
D
and
B
C
∴
A
D
||
B
C
- as alternate angles are equal
As opposite sides of quadrilateral are parallel,
A B C D is a parallelogram
Answer:
i) The policeman said to the thief "I have caught you red-handed".
(ii) The man said, "This is the most beautiful picture I have painted."
(iii) She told me, "You have made a serious mistake.
(iv) He said to us, "I advise you all to do your work regularly".
(v) The trawler said to me, "Thank you"
(vi)
Step-by-step explanation: