Question

Question 67

Fill in the blanks to make the statement true.

In the given figure, $\Delta ARO\cong \Delta$ ___

Answer 1

In $\Delta ARO$ and $\Delta PQO,\angle AOR=\angle POQ$ [vertically opposite angles]

$\angle ARO=\angle PQO={55}^{\circ }$ [given]

$\Rightarrow \angle RAO=\angle QPO$ [Since if two angles of one triangle is equal to the two angles of other triangle then their third angle will also be equal]

Now, in $\Delta ARO$ and $\Delta PQO,\angle AOR=\angle POQ$ [vertically opposite angles]
AO = PO = 2.5 cm
$\angle RAO=\angle QPO$ [proved above]

By AAS congruence criterion, $\Delta ARO\cong \Delta PQO$