In a ` A B C` , find the measures of the angles of the triangle formed by joining the mid-points of the sides of this triangle.

Explanation

`DE||AB`
`FE||BC`
`DF||CA`
`DE||AB`
`BC \and\ CA` tranverse
`/_C D E =/_ B`
`/_CDE=/_A`
`EF||BC,/_A E F =/_C`
`/_ A F E = /_B`
`OF||CA /_B D F = /_C`
` /_BFD=/_A `
`/_B D F + /_ F D E +/_EDC=180^0`
`/_BDF+/_FDE+/_EDC=180^0`
`/_C +/_F O E +/_ B = 180^0`
` /_F D E = 180 − ( /_B + /_C )`
`/_F D E =/_ A`
`/_ D E F = 180^0 − (/_ A + /_C )=/_B`
`/_DEF=180^0-(/_A+/_C)=/_B`
`/_ E F D= 180^0 −(/_A + /_B) = /_A`
`/_D= /_A,/_ E = /_B , /_F = /_C`