Show that the diagonals of a square are equal and bisect each other at right angles

Quadrilaterals are closed figures with four sides. As they have four angles these are also referred to as quadrangles. A parallelogram is also a quadrilateral like the other common quadrilaterals rectangle and square. In this chapter, we shall learn the specific properties of parallelograms and rhombus. Parallelogram Parallelogram, as the name suggests, has a close association with parallel lines. Yes, this four-sided closed figure has parallel lines. In short, it is a closed figure with four sides with each pair of opposite sides parallel to each other. In the figure above, all the shapes have parallel opposite sides, this means that all the closed figure shapes in the image above are parallelograms. Yes, a rectangle and square are also types of parallelograms which show properties peculiar to their names as well. Properties of Parallelogram A parallelogram has four sides and four angles. Sometimes the sides and angles may be equal while sometimes they may be different. The difference in sides and angles gives the final shape a different name. For example Square, rectangle, rhombus etc. The figure above is of a parallelogram PQRS. What do you notice? PQ and RS are opposite sides and are parallel to each other. Another pair of opposite sides PS and QR are also parallel to each other. PQ and PS are adjacent sides, where PS starts when PQ ends. These adjacent sides when intersecting with each other from adjacent angles. In the figure above ∠ P is adjacent to ∠S and ∠Q is adj...

Properties of Parallelogram The properties of a parallelogram help us to identify a parallelogram from a given set of figures easily and quickly. Before we learn about the properties, let us first know about parallelograms. It is a four-sided closed figure with equal and parallel opposite sides and equal opposite angles. Let us learn more about the properties of parallelograms in detail in this article. 1. 2. 3. 4. What are the Properties of Parallelogram? A parallelogram is a type of Parallelogram Angle Properties The important properties of parallelograms related to angles are as follows: • The opposite • All the angles of a parallelogram add up to 360°, i.e., ∠A + ∠B + ∠C + ∠D = 360°. • The consecutive angles of a parallelogram are ∠A + ∠B = 180° ∠B + ∠C = 180° ∠C + ∠D = 180° ∠D + ∠A = 180° Parallelogram Side Properties The opposite sides of a parallelogram are equal and parallel to each other. Observe the following figure to understand the properties of a parallelogram. All the above properties hold true for all types of parallelograms, but now let us also learn about the individual properties of some Properties of a Square • All four sides of a square are equal. • All four angles are equal and of • The diagonals of a square bisect its angles. • Both the diagonals of a square have the same length. • The opposite sides of a square are equal and parallel to each other. Properties of a Rectangle • The opposite sides of a rectangle are equal and parallel. • All four angles...