For the following figure, prove that $A D = B C$ and $∠ A D B = ∠ B C A$ (2 marks)

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Solution

For triangles, $△ A D O and △ B C O$ ,
$O A = O B$ ..... (given)
$D O = C O$ ..... (given)
$∠ A O D = ∠ B O C$ ..... (vertically opposite angles)
$∴ △ A D O ≅ △ B C O$ .... (SAS criterion for congruency) (1 mark)

Hence,
$A D = B C$ (corresponding parts)
$∠ A D O = ∠ B C O$
$or ∠ A D B = ∠ B C A$ ....(corresponding parts) (1 mark)

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