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Равносторонний треугольник
Равносторонний треугольник: понятие. Свойства равностороннего треугольника. Задания для самостоятельной работы.
Равносторонний треугольник: понятие
.tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] { grid-template-columns: minmax(0, 0.745fr) minmax(0, 0.255fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 } .tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="044edb33733d9bbefa0664e58682806e"] { padding: 0; 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}  @media only screen and (min-width: 600px) and (max-width: 781px) { .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="f2e38b585f2ae50d6160ad1a6cd86415"] { display: none; } } @media only screen and (max-width: 781px) { .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] { grid-template-columns: minmax(0, 0.64fr) minmax(0, 0.36fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 } .tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="f2e38b585f2ae50d6160ad1a6cd86415"] {  } .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] { grid-template-columns: minmax(0, 0.5fr) minmax(0, 0.5fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 }    .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] { grid-template-columns: minmax(0, 0.5fr) minmax(0, 0.5fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 } .wp-block-toolset-blocks-grid-column.tb-grid-column[data-toolset-blocks-grid-column="3034fbe886c11054e95b46b09d3e4112"] { display: flex; }   } @media only screen and (max-width: 599px) { .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] { grid-template-columns: minmax(0, 1fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"]  > .tb-grid-column:nth-of-type(1n+1) { grid-column: 1 } .tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="f2e38b585f2ae50d6160ad1a6cd86415"] { display: none; } .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] { grid-template-columns: minmax(0, 1fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"]  > .tb-grid-column:nth-of-type(1n+1) { grid-column: 1 }    .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] { grid-template-columns: minmax(0, 1fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"]  > .tb-grid-column:nth-of-type(1n+1) { grid-column: 1 } .wp-block-toolset-blocks-grid-column.tb-grid-column[data-toolset-blocks-grid-column="3034fbe886c11054e95b46b09d3e4112"] { display: flex; }   } 
Равносторонним (или правильным) называется треугольник, в котором все стороны имеют одинаковую длину. Т.е. AB = BC = AC.
Свойства равностороннего треугольника
.tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] { grid-template-columns: minmax(0, 0.745fr) minmax(0, 0.255fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 } .tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="044edb33733d9bbefa0664e58682806e"] { padding: 0; } .tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="6f7aa995b4cde007d739dd15413d47ab"] { border-radius: 10px;padding: 25px;border: 2px solid rgba( 184, 131, 225, 1 ); } .tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="f2e38b585f2ae50d6160ad1a6cd86415"] { border-radius: 10px;padding: 25px;border: 2px solid rgba( 184, 131, 225, 1 ); } .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] { grid-template-columns: minmax(0, 0.165fr) minmax(0, 0.835fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 }    .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] { grid-template-columns: minmax(0, 0.7fr) minmax(0, 0.3fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 } .wp-block-toolset-blocks-grid-column.tb-grid-column[data-toolset-blocks-grid-column="3034fbe886c11054e95b46b09d3e4112"] { display: flex; }  @media only screen and (min-width: 600px) and (max-width: 781px) { .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="f2e38b585f2ae50d6160ad1a6cd86415"] { display: none; } } @media only screen and (max-width: 781px) { .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] { grid-template-columns: minmax(0, 0.64fr) minmax(0, 0.36fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 } .tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="f2e38b585f2ae50d6160ad1a6cd86415"] {  } .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] { grid-template-columns: minmax(0, 0.5fr) minmax(0, 0.5fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="07f8aeb431eaebc08e04b43ef7abab75"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 }    .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] { grid-template-columns: minmax(0, 0.5fr) minmax(0, 0.5fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] > .tb-grid-column:nth-of-type(2n + 1) { grid-column: 1 } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="63ec21685dacf6d5cb3e9fe97425b15f"] > .tb-grid-column:nth-of-type(2n + 2) { grid-column: 2 } .wp-block-toolset-blocks-grid-column.tb-grid-column[data-toolset-blocks-grid-column="3034fbe886c11054e95b46b09d3e4112"] { display: flex; }   } @media only screen and (max-width: 599px) { .tb-grid,.tb-grid>.block-editor-inner-blocks>.block-editor-block-list__layout{display:grid;grid-row-gap:25px;grid-column-gap:25px}.tb-grid-item{background:#d38a03;padding:30px}.tb-grid-column{flex-wrap:wrap}.tb-grid-column>*{width:100%}.tb-grid-column.tb-grid-align-top{width:100%;display:flex;align-content:flex-start}.tb-grid-column.tb-grid-align-center{width:100%;display:flex;align-content:center}.tb-grid-column.tb-grid-align-bottom{width:100%;display:flex;align-content:flex-end} .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"] { grid-template-columns: minmax(0, 1fr);grid-auto-flow: row } .wp-block-toolset-blocks-grid.tb-grid[data-toolset-blocks-grid="174df407dc98a68120307939f49ce23e"]  > .tb-grid-column:nth-of-type(1n+1) { grid-column: 1 } .tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto}.tb-container .tb-container-inner{width:100%;margin:0 auto} .wp-block-toolset-blocks-container.tb-container[data-toolset-blocks-container="f2e38b585f2ae50d6160ad1a6cd86415"] { display: none; 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}   } 
Свойство 1. В равностороннем треугольнике все углы равны 60°. Т.е. α = β = γ = 60°.
Свойство 2. В равностороннем треугольнике высота, проведенная к любой из сторон, одновременно является биссектрисой угла, из которого она проведена, а также медианой и серединным перпендикуляром.
CD – медиана, высота и серединный перпендикуляр к стороне AB, а также биссектриса угла ACB.
- CD перпендикулярна AB => ∠ADC = ∠BDC = 90°
- AD = DB
- ∠ACD = ∠DCB = 30°
Свойство 3. В равностороннем треугольнике биссектрисы, медианы, высоты и серединные перпендикуляры, проведенные ко всем сторонам, пересекаются в одной точке.
Свойство 4. Центры вписанной и описанной вокруг равностороннего треугольника окружностей совпадают и находятся на пересечении медиан, высот, биссектрис и серединных перпендикуляров.
Свойство 5. Радиус описанной вокруг равностороннего треугольника окружности в 2 раза больше радиуса вписанной окружности.
- R – радиус описанной окружности;
- r – радиус вписанной окружности;
- R = 2r.
Свойство 6. В равностороннем треугольнике, зная длину стороны (условно примем ее за “a”), можно вычислить:
1.Высоту/медиану/биссектрису:
2. Радиус вписанной окружности:
3. Радиус описанной окружности:
4. Периметр:
5. Площадь:
Формулы равностороннего треугольника
