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Mathematics

In the adjoining figure, we find :

In the adjoining figure, we find : Inequalities, Concise Mathematics Solutions ICSE Class 9.

  1. BD = DC

  2. BD < DC

  3. BD > DC

  4. AD = CD

Triangles

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Answer

In △ ABD,

⇒ AD = BD (Given)

⇒ ∠A = ∠B = 60° (Angles opposite to equal sides are equal)

By angle sum property of triangle,

⇒ ∠A + ∠B + ∠D = 180°

⇒ 60° + 60° + ∠D = 180°

⇒ 120° + ∠D = 180°

⇒ ∠D = 180° - 120° = 60°.

Since, each angle of triangle equals 60°.

∴ ABD is an equilateral triangle, AB = BD = DA.

From figure,

BDC is a straight line.

∴ ∠ADB + ∠ADC = 180°

⇒ 60° + ∠ADC = 180°

⇒ ∠ADC = 180° - 60° = 120°.

In △ ADC,

By angle sum property of triangle,

⇒ ∠DAC + ∠ADC + ∠DCA = 180°

⇒ 25° + 120° + ∠DCA = 180°

⇒ 145° + ∠DCA = 180°

⇒ ∠DCA = 180° - 145° = 35°.

Since, ∠DCA > ∠DAC

∴ AD > DC

Since, AD = BD,

∴ BD > DC. (If two angles of a triangle are unequal, the greater angle has the greater side opposite to it.)

Hence, Option 3 is the correct option.

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