Question

In $\Delta RST,RS=5cm,\angle SRT={45}^{\circ },$ and $\angle RST={45}^{\circ }$. Which of the following criterion can be used to construct
$\Delta RST$ ?

• A. $S.A.S.$ criterion
• B. $S.S.S.$ criterion
• C. None of the above.
• D. $A.S.A.$ criterion
  

Answer 1

The correct option is D $A.S.A.$ criterion


Two angles and an included side of
$\Delta RST$ are given. So, the $A.S.A.$ criterion can be used to construct $\Delta RST.$

Step 1: Draw the line segment $RS$ of length $5cm.$

Step 2: Draw a line from point $S$ at an angle of ${45}^{\circ }$ as shown.


Step 3: Draw another line from point $R$ at an angle of
${45}^{\circ }$ and name the point of intersection as $T$ as shown.