Difference between revisions of "Isosceles triangle"
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| − | An '''isosceles triangle''' is a [[triangle]] in which ''at least'' two [[edge]]s have equal [[length]]. Equivalently, an isosceles triangle is one in which ''at least'' two [[angle]]s have equal [[measure]]. [[Equilateral triangle]]s are a special class of isosceles triangles in which all three sides and [[angle]]s are equal. | + | An '''isosceles triangle''' is a [[triangle]] in which ''at least'' two [[edge]]s have equal [[length]]. Equivalently, an isosceles triangle is one in which ''at least'' two [[angle]]s have equal [[measure]]. [[Equilateral triangle]]s are a special class of isosceles triangles in which all three sides and [[angle]]s are equal. Because Isosceles triangles have two sides of equal length, the angles that don't connect them are equal, meaning that if you had the angle that connects them's measure, you would be able to figure out the other two. In more clear definitions: Say we have an isosceles triangle <math>\triangle ABC</math> where <math>AB = AC</math>. You also know that <math>\angle C = 50^\circ</math>. You can then find out angles <math>\angle A</math> and <math>\angle B</math> because those angles are [[congruent (geometry)]], due to <math>AB=AC</math>. <math>180 - 50 = 130 \rightarrow \frac{130}{2} = 65</math>, so angles <math>A</math> and <math>B</math> are each <math>65^\circ</math>. |
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| + | Every isosceles triangle has reflectional [[symmetry]]. The axis of symmetry passes through the vertex which is shared by the edges of equal length, and it is also the triangle's [[median]], [[altitude]], and [[angle bisector]] of that vertex. | ||
| + | {{asy image|<asy>draw((0,0)--(1,0)--(0.5,0.5)--cycle);</asy>|right|An isosceles triangle.}} | ||
| + | ==See Also== | ||
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| + | * [[Isosceles trapezoid]] | ||
[[Category:Definition]] | [[Category:Definition]] | ||
| + | [[Category:Geometry]] | ||
Latest revision as of 22:32, 4 October 2024
This article is a stub. Help us out by expanding it.
An isosceles triangle is a triangle in which at least two edges have equal length. Equivalently, an isosceles triangle is one in which at least two angles have equal measure. Equilateral triangles are a special class of isosceles triangles in which all three sides and angles are equal. Because Isosceles triangles have two sides of equal length, the angles that don't connect them are equal, meaning that if you had the angle that connects them's measure, you would be able to figure out the other two. In more clear definitions: Say we have an isosceles triangle 
where 
. You also know that 
. You can then find out angles 
and 
because those angles are congruent (geometry), due to 
. 
, so angles 
and 
are each 
.
Every isosceles triangle has reflectional symmetry. The axis of symmetry passes through the vertex which is shared by the edges of equal length, and it is also the triangle's median, altitude, and angle bisector of that vertex.
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![[asy]draw((0,0)--(1,0)--(0.5,0.5)--cycle);[/asy]](http://latex.artofproblemsolving.com/7/9/c/79c4904ff735bf765ca842cac6dc281aaf455e43.png)
