Question
In the adjoining figure, $\text{AB}=\text{AD}$ and $\text{CB}=\text{CD.}$ Prove that $\triangle\text{ABC}\cong\triangle\text{ADC.}$
✓
Answer
In the figure,
$\text{AB}=\text{AD},\text{CB}=\text{CD}$
To prove: $\triangle\text{ABC}\cong\triangle\text{ADC}$
Proof: In $\triangle\text{ABC}$ and $\triangle\text{ADC.}$
$\text{AC}=\text{AC}$ (common)
$\text{AB}=\text{AD}$ (given)
$\text{CB}=\text{CD}$ (given)
$\triangle\text{ABC}\cong\triangle\text{ADC}$ (SSS condition)
Hence proved.
$\text{AB}=\text{AD},\text{CB}=\text{CD}$
To prove: $\triangle\text{ABC}\cong\triangle\text{ADC}$
Proof: In $\triangle\text{ABC}$ and $\triangle\text{ADC.}$
$\text{AC}=\text{AC}$ (common)
$\text{AB}=\text{AD}$ (given)
$\text{CB}=\text{CD}$ (given)
$\triangle\text{ABC}\cong\triangle\text{ADC}$ (SSS condition)
Hence proved.
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