a In the figure 1 given below ABCD is a parallelogram P Q are any two points on the sides AB and BC ...

Question

a In the figure 1 given below ABCD is a parallelogram P Q are any two points on the sides AB and BC respectively Prove that area of CPD area of AQD b In the figure 2 given below PQRS and ABRS are parallelograms and X is any the point on the side BR Show that area of AXS area of gm PQRS

Accepted Answer

a Given From fig 1 gm ABCD in which P is a point on AB and Q is a point on BC To prove area of CPD area of AQD Proof CPD and gm ABCD are on the same base CD and between the same parallels AB and CD ar CPD ar gm ABCD 1 AQD and gm ABCD are on the same base AD and between the same parallels AD and BC ar AQD ar gm ABCD 2 from 1 and 2 ar CPD ar AQD Hence proved b From fig 2 Given PQRS and ABRS are parallelograms on the same base SR X is any point on the side BR Join AX and SX To prove area of AXS area of gm PQRS we know that gm PQRS and ABRS are on the same base SR and between the same parallels So ar gm PQRS ar gm ABRS 1 we know that AXS and gm ABRS are on the same base AS and between the same parallels So ar AXS ar gm ABRS ar gm PQRS From 1 Hence proved

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