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命题一:在一切同底且周长相等的锐角三角形中,等腰三角形的面积最大。分析:当底相等,要使周长相等,则只需要不同的三角形两腰之和相等。由三角形的面积公式可知,同底的三角形,底对应的高越大三角形的面积越大。证法1:如图△ABD和△ABE是同一圆的内接三角形,和为同底的等腰三角形,且AB//CD。∴S_(△ABC)=S_(△ABD)∠ADB=∠AEB<∠ACB
Proposition 1: In all acute triangles with the same circumference and the same circumference, the area of the isosceles triangle is the largest. Analysis: the same at the end, to make the same circumference, you only need different triangles equal waist and waist. The triangle area formula shows that at the same end of the triangle, the corresponding base of the larger the greater the larger the triangle area. Method 1: As shown in Figure △ ABD and △ ABE is the same circle of the inscribed triangle, and is the same bottom isosceles triangle, and AB // CD. ∴S_ (Δ ABC) = S_ (Δ ABD) ∠ADB = ∠AEB <∠ACB