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SSS Criteria for Congruency

In the figure...

Question

In the figure, $△ A B C a n d △ B A D h a v e a c o m m a n b a s e A B . G i v e n, A C = B D a n d B C = A D t h e n f r o m t h e f o l l o w i n g s t a t e m e n t s, w h i c h a r e t r u e a n d w h i c h a r e f a l s e ?$

$△ A B C ≅ △ B A D$

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$△ B P A ≅ △ C P B$

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$△ A P B ≅ △ A D P$

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$△ A P D ≅ △ C P B$

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Solution

The correct option is A
$△ A B C ≅ △ B A D$

Given,
$△ A B C a n d △ B A D h a v e a c o m m a n b a s e . A C = B D B C = A D$
In $△ A B C a n d △ B A D$
$A C = B D (G i v e n) B C = A D (G i v e n) A B = A B (C o m m a n b a s e) T h e r e f o r e, △ A B C ≅ △ B A D (S S S)$

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