If two Triangles are equilateral then prove that the ratio of their respective sides,medians,angle bisectors and altitudes are equal - Maths - Triangles

Question

If two Triangles are equilateral then prove that the ratio of
their respective sides,medians,angle bisectors and altitudes are
equal

Anuradha Sharma · Accepted Answer

As we know that for a equilateral triangle the median ,angle
bisector, and altitude are equal ,
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Now ,
Length of AM and DN can be calculated from the right angle triangle ABM and DNE, AM= a2-a22=3a24=32asimilarly , DN =  b2-b22=3b24=32bNow ratio of side, ABDE=ACDF=BCEF=aband as mentioned earlier all median altitude and angle bisector are same so, AMDN=32a32b=abHence , ABDE=ACDF=BCEF=AMDN=abHence proved

If two Triangles are equilateral then prove that the ratio of their respective sides,medians,angle bisectors and altitudes are equal.