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

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