In the adjacent figure, measures of some angles are given. Prove that $∆ A B C ≅ ∆ D C B$ by ASA congruence condition.

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Solution

Step 1: Find the value of $∠ A B C$ and $∠ D C B$
From the figure,
$\begin{array}{rcl} ∠ A B C & = & ∠ A B D + ∠ D B C \\ = & 30 ° + 40 ° \\ = & 70 ° \end{array}$
$\begin{array}{rcl} ∠ D C B & = & ∠ D C A + ∠ A C B \\ = & 40 ° + 30 ° \\ = & 70 ° \end{array}$
Step 2: Proving that $∆ A B C ≅ ∆ D C B$ by ASA congruence condition
$∠ A B C = ∠ D C B$ [ Each angle $70 °$ ]
$B C = C B$ [ Common side ]
$∠ B C A = ∠ C B D$ [ Each angle $40 °$ ]
Therefore, by ASA congruence condition $∆ A B C ≅ ∆ D C B$

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In the adjacent figure, measures of some angles are given. Prove that ∆ABC≅∆DCB by ASA congruence condition.

In the adjacent figure, measures of some angles are given. Prove that $∆ A B C ≅ ∆ D C B$ by ASA congruence condition.