# 等腰梯形

4

## 性質

1. 两条对角线相等。
2. 同一底上的二内角相等。
3. 对角互补，四顶点共圆

1. 两腰相等的梯形是等腰梯形[2]
2. 两条对角线相等的梯形是等腰梯形[8]
3. 同一底上的二内角相等的梯形是等腰梯形[2]

### 尺寸

${\displaystyle h={\sqrt {c^{2}-{\tfrac {1}{4}}{\left(b-a\right)}^{2}}}}$

### 面積

${\displaystyle A={\frac {1}{2}}{\left(a+b\right)}{\sqrt {c^{2}-{\tfrac {1}{4}}{\left(b-a\right)}^{2}}}}$

### 外接圓

${\displaystyle R=c{\sqrt {\frac {ab+c^{2}}{4c^{2}-(a-b)^{2}}}}.}$

## 參考文獻

1. trapezoid. Math Open Ref. [2019-09-08]. （原始内容存档于2018-09-17）.
2. Weisstein, Eric W. (编). Isosceles Trapezoid. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
3. ^ Larson, Ron; Boswell, Laurie. Big Ideas MATH, Geometry, Texas Edition. Big Ideas Learning, LLC (2016). 2016: 398. ISBN 978-1608408153.
4. ^ Michael de Villiers, Hierarchical Quadrilateral Tree. [2019-09-08]. （原始内容存档于2014-12-22）.
5. ^ isosceles trapezoid. [2019-09-08]. （原始内容存档于2016-08-26）.
6. ^ Halsted, George Bruce, Chapter XIV. Symmetrical Quadrilaterals, Elementary Synthetic Geometry, J. Wiley & sons: 49–53, 1896 [2019-09-08], （原始内容存档于2020-12-27）.
7. ^ Whitney, William Dwight; Smith, Benjamin Eli, The Century Dictionary and Cyclopedia, The Century co.: 1547, 1911
8. ^ Weisstein, Eric W. (编). Trapezoid. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
9. ^ Trapezoid at Math24.net: Formulas and Tables [1]页面存档备份，存于互联网档案馆） Accessed 1 July 2014.
10. ^ Weisstein, Eric W. (编). Rectangle. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.