![]() Therefore, we can simply count the amount of triangles and multiply this by 180 to find the sum of interior angles for the polygon in question.Īn example of this for a six-sided shape is shown below.įrom this technique a rule can be found to find the sum of the interior angles for any polygon: we must take two from the number of sides and then multiply by. This will then split the shape into a number of triangles which, as we have already seen, must have interior angles that sum to. The best method for summing the angles that are in any polygon is to choose any of the vertices and then draw lines to all the others from this particular vertex. Below is a list of some more names of polygons that you should try to remember. This means that a triangle is a polygon with three sides and a quadrilateral is a polygon with four sides. PolygonsĪ polygon is just a name for a shape which has all straight sides. Now angle x can be found by using the fact that angles in a quadrilateral add up to so therefore. The angle y can be found using what we know of angles on a straight line. Equal sides are next to each other, not opposite.įind the unknown angles and in the following diagram.Two pairs of sides that are equal in length and parallel.Therefore, a rhombus has all the same properties of a parallelogram as well as having two lines of symmetry.A type of parallelogram that has four equal sides.Each side in a parallelogram is parallel to the side that is opposite.Does not necessarily have any lines of symmetry (although some do).There are many different types of quadrilateral which we will now look at and some of their properties will be explained. This same technique can be done for any quadrilateral, so we can conclude that all quadrilaterals have interior angles that add up to. Therefore, the quadrilateral, which is made of two triangles, must have interior angles that add to. The quadrilateral has been split into two triangles, which must both have interior angles that add up to. To verify this fact we can simply look at any quadrilateral, such as the one below, and put a line through it that splits the shape into two distinct regions. This is similar to how angles in any sized triangle will add to which we have already explored on this course. The angles that are interior in any quadrilateral will always add up to. The only rule is that the four sides cannot be curved in any way: they must all be straight. If we define an isosceles trapezoid to be a trapezoid with congruent base angles, we can easily prove the sides (legs) to also be congruent, a parallelogram will NOT be an isosceles trapezoid, and all of the commonly known properties of an isosceles trapezoid will still be true.Any four-sided shape falls into the category of being a quadrilateral. Since they will not be true for a parallelogram. If this occurs, the other properties that an isosceles trapezoid can possess can no longer hold, If an isosceles trapezoid is defined to be "a trapezoid with congruent legs",Ī parallelogram will be an isosceles trapezoid. Mentions congruent base " angles", not sides (or legs). Note: The definition of an isosceles triangle states that the triangle has two congruent " sides".īut the definition of isosceles trapezoid stated above, An isosceles trapezoid (with only 1 pair of parallel sides) has no rotational symmetry.An isosceles trapezoid has at least 1 axis of reflectional symmetry.An isosceles trapezoid has congruent legs.Definition: An isosceles trapezoid is a trapezoid with congruent base angles.
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