Question

In the following figure, check whether triangles are congruent by ASA congruence condition ? If congruent, write the congruence of two triangles in symbolic form:

Answer 1

STEP 1 : Finding the value of $\angle BAC$ and $\angle DCA$

In $∆ABC$, sum of all its interior angles is$180°$.

Therefore,

$\angle BAC+\angle ACB+\angle B=180°$

$\angle BAC+30°+100°=180°$

$\begin{array}{rcl}\angle BAC& =& 180°-130°\\ & =& 50°\end{array}$

Similarly, In $∆CDA$

$\angle DCA+\angle CAD+\angle D=180°$

$\angle DCA+30°+100°=180°$

.$\begin{array}{rcl}\angle DCA& =& 180°-130°\\ & =& 50°\end{array}$

STEP 2 : Checking that $∆ABC\cong ∆CDA$ or not

Now, In $∆ABC$ and $∆CDA$

$\angle BAC=\angle DCA$ [ Each angle $50°$]

$AC=CA$ [ Common side ]

$\angle ACB=\angle CAD$ [ Each angle $30°$]

Therefore, by ASA congruence condition $∆ABC\cong ∆CDA$