Prove that the base angles of an isosceles trapezium are equal.
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Given : ABCD is a isosceles trapezium.
AB // DC , AD = BC
To prove : <A = <B
Construction : Draw DM and CN
perpendiculars to AB .
Proof : In ∆AMD and ∆BNC
<DMN = <CNB = 90° [ Right angle ]
AD = BC ( given ) [ Hypotenuse ]
DM = CN [ Construction ]
Therefore ,
∆AMD congruent to ∆BNC
[ RHS congruence rule ]
<A = <B [ C.P.CT ]
••••••
AB // DC , AD = BC
To prove : <A = <B
Construction : Draw DM and CN
perpendiculars to AB .
Proof : In ∆AMD and ∆BNC
<DMN = <CNB = 90° [ Right angle ]
AD = BC ( given ) [ Hypotenuse ]
DM = CN [ Construction ]
Therefore ,
∆AMD congruent to ∆BNC
[ RHS congruence rule ]
<A = <B [ C.P.CT ]
••••••
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