Question

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


Pick the correct option.

• 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

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