In the following figures, which pairs of triangles are congruent by SAS congruence condition? If congruent, write the congruence of two triangles in the symbolic form :

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Solution

Checking the congruency:

In $∆ A D B$ and $∆ C B D$ ,
$A D = C B$ [ Each side $4 c m$ ]
$∠ A = ∠ C$ [ Each angle $100 °$ ]
$D B = B D$ [ Common side ]
But here $∠ A$ and $∠ C$ are not the included angles of the two corresponding equal sides.
Also, $∠ A D B$ and $∠ C B D$ are the included angles but we don;t know whether they are equal or not.
Hence, $∆ A D B$ is not congruent to $∆ C B D$

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