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 $\angle B$ and $\angle Q$

In $∆ABC$,

$\angle A+\angle B+\angle C=180°$ [ Angle sum property]

$70°+\angle B+25°=180°$

$\begin{array}{rcl}\angle B& =& 180°-95°\\ & =& 85°\end{array}$

Similarly, In $∆PQR$,

$\angle P+\angle Q+\angle R=180°$ [ Angle sum property ]

$70°+\angle Q+30°=180°$

$\begin{array}{rcl}\angle Q& =& 180°-100°\\ & =& 80°\end{array}$

STEP 2 : Finding that $∆ABC\cong ∆PQR$ or not

Now, In $∆ABC$ and $∆PQR$,

$\angle A=\angle P$ [ Each angle $70°$ ]

$AB=PQ$ [ Each side $4cm$ ]

$\angle B\ne \angle Q$

Therefore, $∆ABC$ is not congruent to $∆PQR$.