Question

A $∆PQR$can be constructed, when $PQ=5.3cm,$$m\angle PQR={105}^o$and $m\angle QRP={40}^o$using the ________ criterion.

• A. $SAS$
• B. $ASA$

Answer 1

The correct option is B

$ASA$

Step-1: Given Information

$PQ=5.3cm,$(one side of the triangle)

$m\angle PQR={105}^O$

$m\angle QRP={40}^o$

Step-2: Find the angle $m\angle RPQ$

$m\angle PQR+m\angle QRP+m\angle RPQ={180}^o$ ( sum of interior angles of a triangle)

${105}^o+{40}^o+m\angle RPQ={180}^o$

${140}^o+m\angle RPQ={180}^o$

$m\angle RPQ={180}^o-{140}^o$

$m\angle RPQ={40}^o$

Step-3: Constructing a triangle

We can Construct a triangle if two angles and a side containing them are given.

Here, Two angles are $m\angle PQR={105}^o$$m\angle RPQ={40}^o$and the side containing them is $PQ=5.3cm,$

Hence, $∆PQR$Triangle can be constructed by $ASA$