As shown in the picture, a triangular piece of land should be evenly divided among farmers a, B and C. If ∠ C = 90 ° and ∠ B = 30 ° and the size and shape of the land obtained by these three farmers are the same, please try to divide it, draw it on the picture and prove it

As shown in the picture, a triangular piece of land should be evenly divided among farmers a, B and C. If ∠ C = 90 ° and ∠ B = 30 ° and the size and shape of the land obtained by these three farmers are the same, please try to divide it, draw it on the picture and prove it


Three congruent triangles are obtained by crossing BC with D and de ⊥ AB with e through D. they are ∵ C = 90 °, B = 30 °, cab = 60 ° and ∵ ad is the angular bisector of BAC. They are ∵ bad = ∵ CAD = 12 ⊥ cab = 30 ° and ∵ CD = 12ad, AC = adcos 30 ° = 32ad, AC = 3CD and s △ ACD = 12 × a



As shown in the picture, divide a triangular piece of land evenly among the three farmers. If ∠ C = 90 ° and ∠ B = 30 °, to make the land of the three farmers the same size and shape, please try to divide it and draw it on the picture


Three congruent triangles are obtained by making the bisector ad of ∠ a intersect BC at D and making de ⊥ AC at e through D
∵ ad is the angular bisector of ∠ BAC, so ∠ CAD = 30 °,
And s △ ACD = × AC × CD;
∵∠ DAE = 30 ° and ∠ DEA = 90 °
It can be proved that △ ACD ≌ △ AED,
Similarly, △ ACD ≌ △ bed,
S△ADE= ×AE×DE=S△BDE= ×BE×DE=S△ACD,
In this way, it can be divided into three lands of the same size and shape



As shown in the picture, a triangle of land should be divided among farmers a, B and C. If angle c is equal to 90 degrees and angle B is equal to 30 degrees, the three farmers should have the same size and shape of land. Please try to divide it and draw it on the picture


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