In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE)

In the given figure, E is any point on median AD of a ΔABC. Show that

ar (ABE) = ar (ACE)

ans)

AD is the median of ΔABC. Therefore, it will divide ΔABC into two triangles of equal areas.

∴ Area (ΔABD) = Area (ΔACD) ... (1)

ED is the median of ΔEBC.

∴ Area (ΔEBD) = Area (ΔECD) ... (2)

On subtracting equation (2) from equation (1), we obtain

Area (ΔABD) − Area (EBD) = Area (ΔACD) − Area (ΔECD)

Area (ΔABE) = Area (ΔACE)

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Project Tiger

Project Tiger is a wildlife conservation movement initiated in India in 1973 to protect tigers . The project aims at tiger conservation in specially constituted tiger reserves representative of various regions throughout India and strives to maintain viable populations of Bengal tigers in their natural environment. In 2008 there were more than 40 Project Tiger reserves covering an area over 37,761 km 2 (14,580 sq mi). Project Tiger helped to increase the population of these tigers from 1,200 in the 1970s to 3,500 in 1990s. However, a 2008 census held by the Government of India revealed that the tiger population had dropped to 1,411. Since then the government has pledged US$153 million to further fund the project, set-up a Tiger Protection Force to combat poachers , and fund the relocation of up to 200,000 villagers to minimize human-tiger conflicts. The number of tigers in India's wild has gone up by 20%, according to...

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