Why quadrilateral is 360

Each triangle has an angle sum of degrees. Therefore the total angle sum of the quadrilateral is degrees. Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram. The correct answer is that all trapezoids are quadrilaterals. Trapezoids are four-sided polygons, so they are all quadrilaterals. This last method can save time and energy when working a proof!

It is true that every rectangle is a parallelogram , but it is not true that every parallelogram is not a rectangle. For instance, take a square. It's a parallelogram — it is a quadrilateral with two pairs of parallel faces. But it is also a rectangle — it is a quadrilateral with four right angles.

A square is a parallelogram. This is always true. A rhombus is a quadrilateral with all sides equal in length.

A square is a quadrilateral with all sides equal in length and all interior angles right angles. Thus a rhombus is not a square unless the angles are all right angles. A square however is a rhombus since all four of its sides are of the same length.

A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram , since it has two pairs of parallel sides. No, because a rhombus does not have to have 4 right angles. Why is the sum of the interior angles of a quadrilateral ? We use first party cookies on our website to enhance your browsing experience, and third party cookies to provide advertising that may be of interest to you.

You can accept or reject cookies on our website by clicking one of the buttons below. To understand more about how we and our advertising partners use cookies or to change your preference and browser settings, please see our Global Privacy Policy. Polygons - Quadrilaterals. Properties of quadrilaterals, interior angles of quadrilaterals Polygons: Properties of Quadrilaterals Sum of the Interior Angles of Quadrilaterals: To find the sum of the interior angles of a quadrilaterals, divide it up into triangles We get So, the sum of the interior angles of a quadrilateral is degrees.

Regular Quadrilaterals - Squares: The properties of squares: All sides are the same length congruent and all interior angles are the same size congruent. The measure of the central angles of a square: To find the measure of the central angle of a square, make a circle in the middle A circle is degrees around Divide that by four angles Sign up Log in.

These add up to degrees e and c are also interior. Any two angles that add up to degrees are known as supplementary angles. Angle Sum of a Triangle Using some of the above results, we can prove that the sum of the three angles inside any triangle always add up to degrees.

If we have a triangle, you can always draw two parallel lines like this: Now, we know that alternate angles are equal. Angle Sum of a Quadrilateral A quadrilateral is a shape with 4 sides. Exterior Angles The exterior angles of a shape are the angles you get if you extend the sides. The exterior angles of a hexagon are shown: A polygon is a shape with straight sides.

Interior Angles The interior angles of a shape are the angles inside it. Exterior Angle of a Triangle Angle x is an exterior angle of the triangle: The exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices.

Proof: The angles in the triangle add up to degrees. The angles on a straight line add up to degrees.