Last updated at Dec. 8, 2016 by Teachoo

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Ex 6.3, 16 If AD and PM are medians of triangles ABC and PQR, respectively where ฮABC โผ ฮPQR, prove that ๐ด๐ต/๐๐ = ๐ด๐ท/๐๐ Given: ฮABC and ฮPQR AD is the median of ฮ ABC ,PM is the median of ฮ PQR & ฮABC โผ ฮPQR. To Prove:- ๐ด๐ต/๐๐=๐ด๐ท/๐๐ Proof: Since AD is the median BD = CD = 1/2 BC Similarly, PM is the median QM = RM = 1/2 QR Now, ฮABC โผ ฮPQR. ๐ด๐ต/๐๐=๐ต๐ถ/๐๐ =๐ด๐ถ/๐๐ So, ๐ด๐ต/๐๐=๐ต๐ถ/๐๐ ๐ด๐ต/๐๐=2๐ต๐ท/2๐๐ ๐ด๐ต/๐๐=๐ต๐ท/๐๐ Also, since ฮABC โผ ฮPQR. โ B = โ Q Now, In ฮ ABD & ฮPQM โ ๐ต=โ ๐ ๐ด๐ต/๐๐=๐ต๐ท/๐๐ Hence by SAS similarly ฮABD โผ ฮPQM Since corresponding sides of similar triangles are proportional ๐ด๐ต/๐๐=๐ด๐ท/๐๐ Hence proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.