a In the figure given ABCD and AEFG are two parallelograms Prove that area of gm ABCD area of gm AE...

Question

a In the figure given ABCD and AEFG are two parallelograms Prove that area of gm ABCD area of gm AEFG b In the fig 2 Given below the side AB of the parallelogram ABCD is produced to E A straight line through A is drawn parallel to CE to meet CB produced at F and parallelogram BFGE is Completed prove that area of gm BFGEArea of gm ABCD c In the figure 3 given below AB DC EF AD BE and DE AF Prove the area of DEFH is equal to the area of ABCD

Accepted Answer

a Given From fig 1 ABCD and AEFG are two parallelograms as shown in the figure To prove area of gm ABCD area of gm AEFG Proof let us join BG We know that ar ABG ar gm ABCD 1 Similarly ar ABG ar gm AEFG 2 From 1 and 2 ar gm ABCD ar gm AEFG So ar gm ABCD ar gm AEFG Hence proved b Given From fig 2 A parallelogram ABCD in which AB is produced to E A straight line through A is drawn parallel to CE to meet CB produced at F and parallelogram BFGE is Completed To prove area of gm BFGEArea of gm ABCD Proof Let us join AC and EF We know that ar AFC ar AFE 1 now subtract ar ABF on both sides we get ar AFC ar ABF ar AFE ar ABF Or ar ABC ar BEF Now multiply by 2 on both sides we get 2 ar ABC 2 ar BEF Or ar gm ABCD ar gm BFGE Hence proved c Given From fig 3 AB DC EF AD BE and DE AF To prove area of DEFH area of ABCD Proof We know that DE AF and AD BE It is given that ADEG is a parallelogram So ar gm ABCD ar gm ADEG 1 Again DEFG is a parallelogram ar gm DEFH ar gm ADEG 2 From 1 and 2 ar gm ABCD ar gm DEFH Or ar ABCD ar DEFH Hence proved

ML Aggarwal Solutions Class 9 Mathematics Solutions for Theorems on Area Exercise 14 in Chapter 14 - Theorems on Area