Question

If the red line divides the parallelogram such that a is 1 3 r d of b and 2 3 r d of c, what is the measure of d?

Answer 1

Answer:

Since ABCD is a parallelogram.

AB∥CD and BD is a transversal

In △ABD and △DCB

∠ABD=∠CBD(alternate interior angles)

AB=CD(opposite sides of a parallelogram)

AD=CB(opposite sides of a parallelogram)

BD=DB(common)

∠ABD≅∠DCB (By SAS)

∴ diagonal BD divides a parallelogram ABCD into two congruent triangles ABD and DCB.

Similarly diagonal AC divides parallelogram ABCD into two congruent triangles ABC and ADC.

Hence the diagonal divides a parallelogram into two triangles of equal areas.

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