Let ABCD be a square and let points P on AB and Q on DC be such that DP = AQ. Prove that BP = CQ.
Answers
Answered by
8
Given :
ABCD is a square .
P and Q are two points on AB and
DC respectively such that DP = AQ.
To prove : BP = CQ
proof :
In ∆DAP and ∆ADQ
<DAP = <ADQ = 90° [Angles in a square]
DP = AQ [ Given ]
AD = DA [ common ]
Therefore ,
∆DAP congruent to ∆ADQ
[ RHS congruence rule ]
AP = DQ [ C.P.CT ] ----( 1 )
AB = CD [ Sides in a square ]
AP + PB = DQ + QC
DQ + BP = DQ + CQ [ from ( 1 ) ]
BP = CQ
•••••
ABCD is a square .
P and Q are two points on AB and
DC respectively such that DP = AQ.
To prove : BP = CQ
proof :
In ∆DAP and ∆ADQ
<DAP = <ADQ = 90° [Angles in a square]
DP = AQ [ Given ]
AD = DA [ common ]
Therefore ,
∆DAP congruent to ∆ADQ
[ RHS congruence rule ]
AP = DQ [ C.P.CT ] ----( 1 )
AB = CD [ Sides in a square ]
AP + PB = DQ + QC
DQ + BP = DQ + CQ [ from ( 1 ) ]
BP = CQ
•••••
Attachments:
Similar questions