Question

Choose the correct options from below:

• A. $PQ<RS$
• B. $QR>PS$
• C. $PQ>RS$
• D. $QR=PS$

Answer 1

Answer: (A), (D)

The correct options are
A $PQ<RS$
D $QR=PS$

• Draw a line segment $PQ$ of length $4.6cm$.
  
• Draw a line at an angle ${30}^o$ taking base $PQ$ and vertex $Q$.
  
• From $P$ mark an arc of length $5.2cm$. This arc cuts the line at ${30}^o$ from $PQ$ at $S$.
  
• Join $PS$ and $PQ$.
  
• Draw perpendicular bisectors of $PQ$ and $SP$. These bisectors meets at point $O$.
  
• Taking $O$ as center, draw a circle of radius $OP$. This circle touches $P,Q,S$.
  
• Draw a line from vertex $S$ and parallel to line $PQ$. This parallel line cuts the circle at point $R$.
  
• Join $PQRS$

From figure it is clear that $RS>PQ$ and $SP=RQ$