Question

$\text{In parallelogram}ABCD,AP\text{and}CQ\text{are perpendicular to diagonal}BD.\text{It can be proved that:}\text{Statement 1:}\Delta APB\cong \Delta CQD,\text{Statement 2: RHS congruence is applied}$

• A. Both statements are correct
• B. Both statements are false
• C. Statement 1 is correct but 2 is false
• D. Statement 1 is false but 2 is correct

Answer 1

The correct option is C Statement 1 is correct but 2 is false

$\text{In}\Delta APB\text{and}\Delta CQD$
AB=CD (Opposite sides of a parallelogram)
$\angle ABP=\angle CDQ$ (Alternate angles)
$\angle APB=\angle CQD$ (Both are right angles)
$\therefore \Delta APB\cong \Delta CQD$ (using AAS criterion)
Hence, statement 1 is correct but statement 2 is false.