Important properties of Geometric Shapes

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Important properties of Geometric ShapesProperties of Triangle

• Sum of the angles of a triangle $=180°$
• Sum of any two sides of a triangle is greater than the third side.
• The line joining the midpoint of a side of a triangle to the positive vertex is called the median.
• The median of a triangle divides the triangle into two triangles with equal areas.
• Centroid is the point where the three medians of a triangle meet.
• Centroid divides each median into segments with a $2:1$ ratio
• Area of a triangle formed by joining the midpoints of the sides of a given triangle is one-fourth of the area of the given triangle.
• An equilateral triangle is a triangle in which all three sides are equal.
• In an equilateral triangle, all three internal angles are congruent to each other.
• In an equilateral triangle, all three internal angles are each $60°$
• An isosceles triangle is a triangle with (at least) two equal sides.
• In isosceles triangle, altitude from vertex bisects the base.

Properties of QuadrilateralsRectangle

• The diagonals of a rectangle are equal and bisect each other.
• opposite sides of a rectangle are parallel.
• opposite sides of a rectangle are congruent.
• opposite angles of a rectangle are congruent.
• All four angles of a rectangle are right angles.
• The diagonals of a rectangle are congruent.

Square

• All four sides of a square are congruent.
• Opposite sides of a square are parallel.
• The diagonals of a square are equal.
• The diagonals of a square bisect each other at right angles.
• All angles of a square are $90$ degrees.
• A square is a special kind of rectangle where all the sides have equal length.

Parallelogram

• The opposite sides of a parallelogram are equal in length.
• The opposite angles of a parallelogram are congruent (equal measure).
• The diagonals of a parallelogram bisect each other.
• Each diagonal of a parallelogram divides it into two triangles of the same area.

Rhombus

• All the sides of a rhombus are congruent.
• Opposite sides of a rhombus are parallel.
• The diagonals of a rhombus bisect each other at right angles.
• Opposite internal angles of a rhombus are congruent (equal in size).
• Any two consecutive internal angles of a rhombus are supplementary; i.e. the sum of their angles $=180°$ (equal in size).
• If each angle of a rhombus is $90°,$ it is a square.

More Properties of Quadrilaterals

• Sum of the interior angles of a quadrilateral is $360$ degrees.
• If a square and a rhombus lie on the same base, area of the square will be greater than area of the rhombus (In the special case when each angle of the rhombus is $90°$, rhombus is also a square and therefore areas will be equal).
• A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
• Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.
• Each diagonal of a parallelogram divides it into two triangles of the same area.
• A square is a rhombus and a rectangle.