Ex 6.3, 16 - If AD and PM are medians of triangles ABC, PQR - Given similar, find angles or sides

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Ex 6.3, 16 If AD and PM are medians of triangles ABC and PQR, respectively where ฮ”ABC โˆผ ฮ”PQR, prove that ๐ด๐ต/๐‘ƒ๐‘„ = ๐ด๐ท/๐‘ƒ๐‘€ Given: ฮ”ABC and ฮ”PQR AD is the median of ฮ” ABC ,PM is the median of ฮ” PQR & ฮ”ABC โˆผ ฮ”PQR. To Prove:- ๐ด๐ต/๐‘ƒ๐‘„=๐ด๐ท/๐‘ƒ๐‘€ Proof: Since AD is the median BD = CD = 1/2 BC Similarly, PM is the median QM = RM = 1/2 QR Now, ฮ”ABC โˆผ ฮ”PQR. ๐ด๐ต/๐‘ƒ๐‘„=๐ต๐ถ/๐‘„๐‘…=๐ด๐ถ/๐‘ƒ๐‘… So, ๐ด๐ต/๐‘ƒ๐‘„=๐ต๐ถ/๐‘„๐‘… ๐ด๐ต/๐‘ƒ๐‘„=2๐ต๐ท/2๐‘„๐‘€ ๐ด๐ต/๐‘ƒ๐‘„=๐ต๐ท/๐‘„๐‘€ Also, since ฮ”ABC โˆผ ฮ”PQR. โˆ  B = โˆ  Q Now, In ฮ” ABD & ฮ”PQM โˆ ๐ต=โˆ ๐‘„ ๐ด๐ต/๐‘ƒ๐‘„=๐ต๐ท/๐‘„๐‘€ Hence by SAS similarly ฮ”ABD โˆผ ฮ”PQM Since corresponding sides of similar triangles are proportional ๐ด๐ต/๐‘ƒ๐‘„=๐ด๐ท/๐‘ƒ๐‘€ Hence proved

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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.