Geometry is derived from a Greek word that means ‘Earth Measurement’. It is a branch of mathematics and is concerned with the properties of space i.e., a visual study of shapes, position of figures, patterns, sizes, etc. Geometry is a subject of countless developments, so there exist many types. They are Euclidean Geometry, Non-Euclidean Geometry, Algebraic Geometry, Riemannian Geometry, and Symplectic Geometry. QuadrilateralA quadrilateral can be separated into two words Quad means four and lateral means side. So a quadrilateral is a closed figure with four sides. It had four vertices. The sides of a quadrilateral are equal/ unequal/ parallel/ irregular which leads to various geometric figures. Example: Square, Rectangle, Rhombus, Parallelogram, Trapezium, etc. The midpoint of a side divides a side of any figure into two equal parts (length-wise). In a quadrilateral, there will be a midpoint for each side i.e., Four mid-points. There are a few factors that determine the shape formed by joining the midpoints of a quadrilateral. Those factors are the kind of quadrilateral, diagonal properties, etc. These factors affect the shape formed by joining the midpoints in a given quadrilateral. Let’s look into the various scenarios to get a better understanding. Solution:
Sample QuestionsQuestion 1: Consider the rhombus ABCD which is also a kind of Quadrilateral. Find the shape of the figure formed by joining the midpoints. Solution:
Question 2: If the figure formed by joining the midpoint of a quadrilateral is square only if, do explain the condition. Solution:
Question 3: What is the figure formed by joining the midpoints of a parallelogram. Solution:
Question 4: What is the figure formed by joining the midpoints of a quadrilateral whose diagonals are of length equal? Answer:
Question 5: What is the figure formed by joining the midpoints of a quadrilateral whose diagonals are perpendicular but not of equal length? Answer:
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