![]() ![]() The flowchart below shows the different categories into which quadrilaterals can be classified based on the presence of parallel lines. If a quadrilateral has no parallel sides, but both the pairs of adjacent sides are equal, then the quadrilateral can be classified as a kite. ![]() Now, the parallelogram further can be classified which will be covered in a separate topic completely. If a quadrilateral has four parallel lines (or two pairs of parallel lines), then the quadrilateral can be classified as a parallelogram. If a quadrilateral has two parallel lines (or one pair of parallel lines), the quadrilateral can be classified as a trapezoid. One of the angles of quadrilateral labeled as G measures more than 18 0 ∘ 180^\circ 1 8 0 ∘, so G is a concave quadrilateral.Īlso, based on the presence of the number of parallel lines, a quadrilateral can be classified. So, these polygons are quadrilaterals.įurther, all the angles of quadrilaterals labeled as C, E, F, and H measure less than 18 0 ∘ 180^\circ 1 8 0 ∘, so these are convex quadrilaterals. In the given figure, there are 5 polygons, labeled as C, E, F, G, and H, that have 4 sides each. Please ensure Javascript is enabled for purposes of website accessibility. In the given figure, the dotted lines shows the diagonal of the quadrilateral such that one diagonal lies completely outiside the figure.Ĭonsider the eight polygons shown in the figure below: In this example, a kite has two angles labeled with variables. The measure of at least one of the interior angles of a concave quadrilateral is more than 18 0 ∘ 180^\circ 1 8 0 ∘. In the given figure, the dotted lines shows the diagonal of the quadrilateral that lies completely inside the figure.Ĭoncave Quadrilateral: A concave quadrilateral is a quadrilateral in which the diagonal can lie partly or almost outside the figure. ![]() The measure of each of the interior angles of a convex quadrilateral is less than 18 0 ∘ 180^\circ 1 8 0 ∘. Quadrilaterals can be classified into two categories, as shown:Ĭonvex Quadrilateral: A convex quadrilateral is a quadrilateral where the diagonals are completely contained inside it. Therefore, the diagonals of a quadrilateral ABCD are AC and BD. Hence, the diagonals of the quadrilateral are formed by joining A to C and B to D as shown below: For the quadrilateral ABCD, the vertex that is non-adjacent to A is C, and the vertex that is non-adjacent to B is D. That is, ∠ A ∠ B ∠ C ∠ D = 360 ∘ \angle A \angle B \angle C \angle D=360^\circ ∠ A ∠ B ∠ C ∠ D = 3 6 0 ∘.Ī line segment that connects two non-adjacent vertices of the polygon is known as the diagonals of the polygon. The angle sum property of a quadrilateral states that the sum of all the interior angles of a quadrilateral is always 36 0 ∘ 360^\circ 3 6 0 ∘.įor the given quadrilateral ABCD, the sum of the measure of angle A, angle B, angle C, and angle D is 36 0 ∘ 360^\circ 3 6 0 ∘. Therefore, the given quadrilateral can be named as BADC or BCDA. For example, the vertices of the quadrilateral below are B, A, D, and C as shown below: To name a quadrilateral, one should list the names of the vertices either clockwise or counterclockwise. ![]()
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