Question

In the given figure, QTSR is a parallelogram. PQR is a straight line and QU = UT. Which of the following statements are correct?

• A. $△PQU\cong △STU$
• B. $QU=US$
• C. $PQ=QR$
• D. $PU=US$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $△PQU\cong △STU$
C $PQ=QR$
D $PU=US$

Given, QTSR is a parallelogram
$\Rightarrow$ QR = TS and QT = RS

Consider $△PQU\text{and}△STU$

• $\angle PUQ=\angle SUT$..... (vertically opposite angles)
• $QU=UT$ .... (given)
• $\angle PQU=\angle STU$ ....... (alternate interior angles)

$\Rightarrow △PQU\cong △STU$ .....( ASA criterion)

• PU = SU ...... (corresponding parts of congruent triangles)
• PQ = TS ...... (corresponding parts of congruent triangles)
• TS=QR .........(opposite sides of a parallelogram)
• $\Rightarrow PQ=TS=QR$