ABC is a triangle in which AB = AC and D is any point on BC. Prove that
AB AD BD CD
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Answer:
Step-by-step explanation:
Given: ΔABC in which AB=AC and D is a point on the side AC such that BC
2
=AC×CD
To prove: BD=BC
Construction: Join BD
Proof: We have,
BC
2
=AC×CD⇒
CD
BC
=
BC
AC
........(1)
Thus in Δle ABC and Δle BDC we have,
BC
AC
=
CD
BC
........From(1)
and ∠C=∠C (common angle)
∴ΔABC≅ΔBDC [By SAS criterion]
BD
AB
=
CD
BC
...........(2)
From (1) and (2) we get
BC
AC
=
BD
AB
∴BD=BC(∵AB=AC)
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