Answer the following in True or False. Write the reason of your answer (if possible).
(i) The ratio of the corresponding sides of two similar triangles is 4 : 9. Then the ratio of the areas of these triangles is 4 : 9.
(ii) In two triangles respectively ΔABC and ΔDEF of 
then ΔABC ≅ ΔDEF.
(iii) The ratio of the areas of two similar triangles in proportional to the squares of their sides.
(iv) If ΔABC and ΔAXY are similar and the values of their areas are the same then XY and BC may be coincident sides.
(i) False
The ratio of areas of two similar triangles is equal to the ratio of square of their corresponding sides.
So, in the given question the ratio of areas should be 16:81.
(ii) False
The ratio of areas of two similar triangles is equal to the ratio of square of their corresponding sides.
In two triangles respectively ΔABC and ΔDEF of 
then ΔABC~ΔDEF.
(iii) True
(iv) True
In the ΔABO & ΔOCD,
∠AOB = ∠DOC |vertically opp. angles
As AB||CD
∠ABO = ∠DCO |alternate angles
ΔABO~ΔOCD
The sides BC and XY may or may not be coincident.
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
