Question

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

S1 : $△$APD $\cong$ $△$BQC

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

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

Answer 1

The correct option is D

S1 and S2 are 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 ASA criteria

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

Adding ar(PBCD) on both sides of the equation

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

$\Rightarrow$ar($△$APD) + ar(PBCD) = ar($△$BQC) + ar(CDPB)

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