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Standard VII

Mathematics

SAS Criteria for Congruency of Triangles

In the given ...

Question

In the given figure, $A B$ is parallel to $D C .$ If $O A = (3 x - 4) c m, O B = (x + 3) c m, O C = 6 c m$ and $O D = 3 c m,$ find $x .$

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Solution

In $△ O C D$ and $△ O A B$ ,

$∠ A O B = ∠ C O D$ (Vertically opposite angles)
$∠ O C D = ∠ O A B$ (Alternate angles)
$∠ O D C = ∠ O B A$ (Alternate angles)
Thus, $△ O C D \sim △ O A B$ (AAA rule)
Hence, $\frac{O C}{O A} = \frac{O D}{O B}$
$\frac{6}{3 x - 4} = \frac{3}{x + 3}$
$6 x + 18 = 9 x - 12$
$3 x = 30$
$x = 10$

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