Question

Given below are measurements of some parts of two triangles. By drawing their rough figure, examine whether the two triangles are congruent or not by ASA congruence rule. In case of congruence, write it in symbolic form.

$∆DEF$
$\angle D=60°,\angle F=80°,DF=5cm$

$∆PQR$
$\angle Q=60°,\angle R=80°,QR=5cm$

Answer 1

Step 1: Drawing the rough figure

Step 2: Checking whether $∆DEF\cong ∆QPR$ or not

In $∆DEF$ and $∆QPR$,

$\angle D=\angle Q$ [ Each angle $60°$]

$DF=QR$ [ Each side $5cm$]

$\angle F=\angle R$ [ Each angle $80°$]

Since, the two angles and the included side of one triangle is equal to the two angles and the included side of other triangle.

Therefore, by ASA congruence condition $∆DEF\cong ∆QPR$