2. Prove that: Ratio of areas of two triangles is equal to the ratio of the products and corresponding heights
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Answer:
Proof: △ABC∼△DEF
DE
AB
=
EF
BC
⇒
DE
AB
=
2EY
2BX
(∵AX and DY medians BC=2BX,EF=2EY)
⇒
DE
AB
=
EY
BX
...(i)
In △ABX and △DEY
∠B=∠E (∵△ABC∼△DEF)
DE
AB
=
EY
BX
SAS similarity criterion
△ABX∼△DEY
DE
AB
=
DY
AX
...(ii)
Ratio of areas of two similar triangles is equal to ratio of squares of their corresponding sides
ar.△DEF
ar.△ABC
=
DE
2
AB
2
=
DY
2
AX
2
Step-by-step explanation:
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