1.

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

Answer» Given D,E,F are mid point AB,BC and CA
DE||AB,FE||BC and DF||CA
DE||AB and BC and CA tranverse
`/_CDE=/_B`
`/_CED=/_A`
EF||BC `/_AEF=/_C` and `/_AFE=/_B`
OF||CA `/_BDF=/_C` and `/_BFD=/_A`
`/_BDF+/_FDE+/_EDC=180^@`
`/_C+/_FOE+/_B=180^@`
`/_FDE=180-(/_B+/_C)`
`/_FDE=/_A`
`/_DEF=180^@-(/_A+/_C)=/_B`
`/_EFD=180^@-(/_A+/_B)=/_A`
`/_D=/_A,/_E=/_B,/_F=/_C`.


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