The diagonal BD of a quadrilateral ABCD, bisects i) AB =BC ii) AD =CD
Answers
Answered by
9
Step-by-step explanation:
Given A quadrilateral ABCD in which the diagonal BD bisects ∠B and ∠D.
To prove
BC
AB
=
CD
AD
.
Construction Join AC intersecting BD in O.
Proof In △ABC, BO is the bisector of ∠B.
∴
OC
AO
=
BC
BA
⇒
OC
AO
=
BC
AB
...........(i)
In △ADC, DO is the bisector of ∠D.
∴
OC
AO
=
DC
DA
⇒
OC
AO
=
CD
AD
...........(ii)
From (i) and (ii), we get
BC
AB
=
CD
AD
[Hence proved]
Answered by
1
Answer:
ANSWER
In △ABD and △CBD,
BD=BD (Common)
∠ABD=∠CBD (BD bisects ∠B)
∠ADB=∠ADC (BD bisects ∠D)
Thus, △ABD≅△CBD (ASA postulate)
Hence, AB=BC and AD=CD (Corresponding sides)
or AB×CD=BC×AD
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