What are the properties of a parallelogram?

A parallelogram (both pairs of opposite sides parallel) has these properties: (1) Opposite sides are equal (AB = CD, BC = AD); (2) Opposite angles are equal (∠A = ∠C, ∠B = ∠D); (3) Adjacent/consecutive angles are supplementary (∠A + ∠B = 180°); (4) Diagonals bisect each other (each diagonal cuts the other into two equal halves at the point of intersection).

What is the difference between a rhombus and a square?

Both are parallelograms with all four sides equal. Difference: A rhombus has all sides equal but angles are NOT necessarily 90° — opposite angles are equal and adjacent angles are supplementary. A square is a special rhombus where all angles are exactly 90°. So a square is always a rhombus, but a rhombus is not always a square.

State the mid-point theorem.

The mid-point theorem states: 'The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and is half of it.' If in triangle ABC, M is the midpoint of AB and N is the midpoint of AC, then MN is parallel to BC and MN = BC/2. The converse is also true: a line through the midpoint of one side, parallel to another side, bisects the third side.

Properties of Parallelogram

Quadrilaterals • Class 9 Mathematics • NCERT • CBSE

A parallelogram has both pairs of opposite sides parallel. Key properties: opposite sides are equal, opposite angles are equal, diagonals bisect each other. The mid-point theorem states that the line segment joining midpoints of two sides of a triangle is parallel to the third side and half of it.

Key Formulas

∠A + ∠B = 180° (co-interior angles in parallelogram)

Frequently Asked Questions

What are the properties of a parallelogram?: A parallelogram (both pairs of opposite sides parallel) has these properties: (1) Opposite sides are equal (AB = CD, BC = AD); (2) Opposite angles are equal (∠A = ∠C, ∠B = ∠D); (3) Adjacent/consecutive angles are supplementary (∠A + ∠B = 180°); (4) Diagonals bisect each other (each diagonal cuts the other into two equal halves at the point of intersection).
What is the difference between a rhombus and a square?: Both are parallelograms with all four sides equal. Difference: A rhombus has all sides equal but angles are NOT necessarily 90° — opposite angles are equal and adjacent angles are supplementary. A square is a special rhombus where all angles are exactly 90°. So a square is always a rhombus, but a rhombus is not always a square.
State the mid-point theorem.: The mid-point theorem states: 'The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and is half of it.' If in triangle ABC, M is the midpoint of AB and N is the midpoint of AC, then MN is parallel to BC and MN = BC/2. The converse is also true: a line through the midpoint of one side, parallel to another side, bisects the third side.

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