Question

5. verify each statement by measurement. (i) AC + BD = AD + BC A B C D Fig. 12 (ii) AB + CD = AD - BC A​

Answer 1

From the figure,

By using the divider and ruler we measured the given figure,

So,

AB = 1.8 cm, BC = 0.8 cm, BD = 2.7 cm CD = 1.9 cm, AC = 2.6 cm and AD = 4.5 cm

(i) AC + BD = AD + BC

Consider Left hand side (LHS) = AC + BD

= 2.6 cm + 2.7 cm

= 5.3 cm

Now, Right hand side (RHS) = AD + BC

= 4.5 cm + 0.8 cm

= 5.3 cm

By comparing LHS and RHS

LHS = RHS

5.3 cm = 5.3 cm

Therefore, AC + BD = AD + BC

(ii) AB + CD = AD – BC

Consider Left hand side (LHS) = AB + CD

= 1.8 cm + 1.9 cm

= 3.7 cm

Now, Right hand side (RHS) = AD – BC

= 4.5 cm – 0.8 cm

= 3.7 cm

By comparing LHS and RHS

LHS = RHS

3.7 cm = 3.7 cm

Therefore, AB + CD = AD – BC

Answer 2

Answer: i) Now from the figure we've,  

AC+BD

=AC+(BC+CD) [ Since BD=BC+CD]

=(AC+CD)+BC

=AD+BC.

So (i) is true.

ii) Again  

AD−BC

=(AB+BC+CD)−BC [ Since AD=AB+BC+CD]

=AB+CD.

So (ii) is also true.