In the following fig. if AB = AC and BD = DC then $∠ A D C =$

60^{\circ}

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120^{\circ}

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90^{\circ}

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None

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Solution

The correct option is C $90^{\circ}$
Given that, in $△ A B C$ ,
$A B = A C, B D = D C$
To find out: $∠ A D C$

In $△ A D B$ and $△ A D C$ ,
$A B = A C [g i v e n]$
$B D = D C [g i v e n]$
Also, $A D = A D [c o m m o n]$
$∴$ By $S S S$ congruence criterion, $Δ A D B ≅ Δ A D C$ .

Hence, $∠ A D B = ∠ A D B$
Also, $∠ A D B + ∠ A D C = 180^{\circ} [l i n e a r p a i r]$
$∴ ∠ A D B = ∠ A D C = 90^{\circ}$
Hence, $∠ A D C = 90^{\circ}$

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In the following fig. if AB = AC and BD = DC then ∠ADC=

The correct option is C 90∘Given that, in △ABC,AB=AC, BD=DC To find out: ∠ADCIn △ADB and △ADC,AB=AC[given] BD=DC[given]Also, AD=AD[common]∴ By SSS congruence criterion, ΔADB≅ΔADC.Hence, ∠ADB=∠ADBAlso, ∠ADB+∠ADC=180∘[linear pair]∴ ∠ADB=∠ADC=90∘Hence, ∠ADC=90∘

In the following fig. if AB = AC and BD = DC then $∠ A D C =$