in an isoceles triangle ABC if AB=AC and D is a point on BC then prove that
AB ^2-AD^2=BD.CD
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To prove: AB 2 -AD 2 = BD . CD
Construction: Draw AE perpendicular to BC.
Proof: In tr. AEB and tr. AEC,
AB= AC [given]
∠AEB = ∠AEC = 90°
AE= AE [common]
∴ΔAEΔAEC [By RHS]
⇒BE= EC[cpct]
in tr. ABE,
∠E= 90°
Construction: Draw AE perpendicular to BC.
Proof: In tr. AEB and tr. AEC,
AB= AC [given]
∠AEB = ∠AEC = 90°
AE= AE [common]
∴ΔAEΔAEC [By RHS]
⇒BE= EC[cpct]
in tr. ABE,
∠E= 90°
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