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I got here a presentation more or less we come a proving and derivation of ratio and proportion...
let say..an isoseles triangle ABC  where C in vertical that is perpendiular to  point E (  base mid of  AB) , WHOSE ALTItude is 30cm, at angle B has a slant line whose distance is 20 perpndicular to point D (mid of Slope /line AC) angle ABD.(small triangle)
i pressume angle A would be the base angle of the triangle.

here are the ratio and proportion;

30/AE =20/AD;
AD/AE =20/30 =2/3
of course we believe this Phytagorean theorem;
angle ABD;
[AB]^2=20^2 + [AD]^2..........2.

tan A =30/EB (angle ABD) =30/AE (angle AED);
hence: 30/EB= 30/AE;
AE=EB ..(as a proof , u can see that if you draw the triangle)
also we have this arrangement of triangle ABC..

@2 &1
[2AE]^2=400 +[ 4AE^2]/9;
4AE^2=400 +[4AE^2]/9;
36AE^2=3,600 +4AE^2;

tan A= 30/10.6

A=71 degrees;;
the smaller angle of ABD is

90-71 = 19 degrees...

Just take a review , so much the better if i can post my figure for you analize more , algebraically...ty 9 i dont have a sci cal..) 

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