In the figure, $A B C D$ is a rhombus. Are $△ A D C$ and $△ A B C$ congruent? What can you say about $△ A B D$ and $△ B C D$ ?

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Solution

REF.Image.
As it is c rhombus
so all the sides will
be equal
and 1/5 $△ A D C$ and $△ A B C$ are congruent.
$∠ B A C = ∠ C A D$
$∠ D C A = ∠ B C A$
AC $\to$ common in both triangle
So it congruent by ASA (Angle side angle criteria)
Similarly $△ A B D$ and $△ B C D$
are congruent
by ASA criteria
$D B \to$ common side
$∠ A D B = ∠ C D B$
$∠ A B D = ∠ C B D$

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