Are you curious to know what is convex quadrilateral? You have come to the right place as I am going to tell you everything about convex quadrilateral in a very simple explanation. Without further discussion let’s begin to know what is convex quadrilateral?
In the realm of geometry, quadrilaterals are polygons with four sides. They come in various forms, each with its own unique properties and characteristics. In this blog, we will focus on a specific type of quadrilateral known as a convex quadrilateral. We will explore what convex quadrilaterals are, their defining features, and some examples to deepen our understanding of this geometric shape.
What Is Convex Quadrilateral?
A convex quadrilateral is a four-sided polygon where all the interior angles are less than 180 degrees. In simpler terms, it is a quadrilateral whose vertices (corner points) are “pushed outward,” creating a shape that does not fold inward. The opposite of a convex quadrilateral is a concave quadrilateral, which has at least one interior angle greater than 180 degrees.
Properties Of Convex Quadrilaterals
- Interior Angles: In a convex quadrilateral, the sum of the interior angles is always 360 degrees. Each angle is less than 180 degrees, which means that no angle “bends” inward.
- Exterior Angles: The exterior angles of a convex quadrilateral are obtained by extending the sides of the shape. The sum of the exterior angles is always 360 degrees, just like the sum of the interior angles.
- Diagonals: A convex quadrilateral has two diagonals, which are line segments connecting opposite vertices. These diagonals intersect inside the shape, dividing it into four triangles. The intersection point is called the point of concurrency.
- Side Lengths: The side lengths of a convex quadrilateral can vary. It is possible for all sides to have different lengths or for some sides to be equal in length, depending on the specific shape.
Examples Of Convex Quadrilaterals
- Square: A square is a classic example of a convex quadrilateral. It has four equal sides and four right angles (90 degrees). All angles in a square are less than 180 degrees, meeting the criteria of convexity.
- Rectangle: Similar to a square, a rectangle is a convex quadrilateral with four right angles. However, a rectangle does not necessarily have equal side lengths. Opposite sides are parallel and equal in length, while adjacent sides are perpendicular.
- Parallelogram: A parallelogram is another example of a convex quadrilateral. It has two pairs of parallel sides, and opposite angles are equal. The angles inside a parallelogram can vary, but they are always less than 180 degrees.
- Trapezoid: A trapezoid is a convex quadrilateral with one pair of parallel sides. The other two sides are non-parallel and can have different lengths. The interior angles of a trapezoid add up to 360 degrees.
Convex quadrilaterals are a fascinating subset of polygons, distinguished by their outward-pushing vertices and interior angles that are less than 180 degrees. These shapes possess unique properties, such as the sum of interior and exterior angles totaling 360 degrees and the presence of diagonals that intersect inside the shape. Recognizing and understanding convex quadrilaterals, along with their various examples, allows us to appreciate the diversity and beauty found within the realm of geometric shapes.
What Is Convex Quadrilateral With Example?
A convex quadrilateral is a four-sided polygon that has four interior angles that each measure less than 180 degrees. They include specific shapes like rectangles, squares, parallelograms, rhombuses, kites, and trapezoids.
Why Square Is Called Convex Quadrilateral?
A rectangle is a convex quadrilateral since its vertex are raised and both of its diagonals lie in its interior. Also, each interior angle of a rectangle measures 90 degrees. Hence, none of the angles is a reflex angle. So, a rectangle is considered a convex quadrilateral.
What Is A Convex And Non Convex Quadrilateral?
A polygon is convex if all the interior angles are less than 180 degrees. If one or more of the interior angles is more than 180 degrees the polygon is non-convex (or concave). All triangles are convex It is not possible to draw a non-convex triangle. These quadrilaterals are convex This quadrilateral is non-convex.
What Are 2 Examples Of Convex?
Some convex lens uses are listed in the points below.
- Magnifying glasses.
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What Is A Convex Quadrilateral
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What Is The Sum Of The Measure Of The Angles Of A Convex Quadrilateral
What Is Convex Quadrilateral