幾何等腰三角形

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1)設 AB = x , BD = y ,
則 AC = x + y在 AC 上取點 E , 使AE = x , EC = y ,
則 ㄥBAD = ㄥEAD = 30° (已知)
AD = AD (公共)
AB = AE = x
故
△ADB ≡ △ADE (S.A.S.)對應邊 BD = DE = y又EC = AC - AE = (x + y) - x = y故 △ EDC 等腰 ,ㄥECD + ㄥEDC = ㄥAED (△外角和)
ㄥECD + ㄥEDC = θ
故 ㄥECD = ㄥEDC = θ/2 (等腰△底角)ㄥB = ㄥAED = θ (全等△對應角)ㄥA + ㄥB + ㄥC = 180° (△內角和)60° + θ + θ/2 = 180°θ = 80°ㄥB = 80° 2)因腰上的高與等腰三角形底邊的夾角是45° , 故底角 = 180° - 90° - 45° = 45°故此它是等腰直角三角形,面積 = 腰 x 腰 / 2 = 1 x 1 / 2 = 1/2。