Question

In the given figure, ABCD is a parallelogram and PD is parallel to QC.

S1 : $△$APD $\cong$ $△$BQC

S2 : area($△$APD) + area(PBCD) = area($△$BQC) + area(CDPB)

• A. S1 is true but S2 is false
• B. S1 is false but S2 is true
• C. Both S1 and S2 are false
• D. S1 and S2 are both true and S1 is the explanation for S2

Answer 1

The correct option is D

S1 and S2 are both true and S1 is the explanation for S2

In $△$APD and $△$BQC

$\angle PAD=\angle QBC$ (corresponding angles)

AD = BC ( opp. sides of parallelogram)

$\angle APD=\angle BQC$ (corresponding angles)

$△APD\cong △BQC$ by AAS criteria

And area($△$APD) = area($△$BQC) (congruent triangles have equal areas)

Adding area(PBCD) on both sides of the equation

area($△$APD) + area(PBCD) = area($△$BQC) + area(PBCD)

Therefore, both S1 and S2 are true and S1 is the explanation of S2.