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As shown in the figure, in △ ABC, de and FG are the vertical bisectors of AB and AC, respectively. If BC = 10, what is the perimeter of △ ADF?
∵ de and FG are the vertical bisectors of AB and AC of △ ABC ∵ ad = BD, AF = CF ∵ ADF perimeter = AD + DF + AF = BD + DF + CF = BC = 10 ∵ ADF perimeter is 10
As shown in the figure, ∠ BAC = 106 ° in △ ABC, de and FG are the vertical bisectors of AB and AC respectively, then ∠ EAG=______ ．
In △ ABC, ∠ BAC = 120 °, ∫ B + ∠ C = 180 ° - 120 ° = 60 °, ∫ De is the vertical bisector of AB, ∫ EB = EA, ∫ 1 = ∠ B, similarly, ∫ 2 = C, and ∫ 1 + 2 + B + C + EAG = 180 °, ∫ 2 (∫ B + ∠ C) + EAG = 180 ° and ∫ EAG = 60 °
In the triangle ABC, the angle ACB = 90 degrees, D is a point on the extension line of BC, e is the intersection of the vertical bisector of BD and AB, de intersects AC at F, then e must be in the vertical bisector of AF
Because e is on the vertical line of BD
So, ed = EB
So, angle d = angle B
Because angle B + angle a = 90 degrees, angle D + angle DFC = 90 degrees
So angle a = angle DFC
And because the angle AFE = the angle DFC
So, angle a = angle AFE
So EAF is an isosceles triangle
So EA = EF
So e is on the AF bisector
Ask me online if I can't understand
As shown in the figure, in the triangle ABC, BC is equal to 7, the vertical bisectors of AB intersect abbc at point de, and the vertical bisectors of AC intersect DEBC at point FG
If the angle BAC is equal to 106 ° then the degree of the angle EAG is?
32°
Because the angle B is equal to ∠ BAC, ∠ C is equal to ∠ GAC, ∠ BAC + ∠ GAC = ∠ BAC + ∠ EAG ∠ B + ∠ C = 180-106 = 74
Therefore, EAG = 106-74 = 32
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