mid - point theorem🔥| examples | Quadrilaterals😍| Chapter - 8 |

mid - point theorem🔥| examples | Quadrilaterals😍| Chapter - 8 | #quadrilaterals #class9thmaths




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The Mid-point Theorem:

Theorem 8.8 : The line segment joining the mid-points of two sides of a triangle is parallel to the third side.




Theorem 8.9 : The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.




Example 6 : In ∆ ABC, D, E and F are respectively the mid-points of sides AB, BC and CA (see Fig.). Show that ∆ ABC is divided into four congruent triangles by joining D, E and F.






Quadrilateral:


A quadrilateral is a two-dimensional, closed shape with four sides, four vertices (or corners), and four angles. The sum of the interior angles in any quadrilateral is always 360 degrees. They are a type of polygon.

Here's a breakdown:

Definition: A quadrilateral is a four-sided polygon.
Sides: It has four straight sides.
Angles: It has four angles.
Vertices: It has four vertices (corners).
Angle Sum: The total measure of all interior angles is 360 degrees.

Examples: Common types include squares, rectangles, parallelograms, rhombuses, trapezoids, and kites.


#parallelogram :


A parallelogram is a four-sided flat shape (quadrilateral) with opposite sides that are parallel and equal in length. Key properties include opposite angles being equal and diagonals that bisect each other. Special types of parallelograms include rectangles, rhombuses, and squares.

Key Properties of a Parallelogram:
Opposite sides are parallel: This is the defining characteristic, giving the shape its name.
Opposite sides are equal in length: Each pair of parallel sides has the same length.
Opposite angles are equal: The angles opposite each other within the parallelogram are congruent.
Diagonals bisect each other: The lines connecting opposite corners intersect at their midpoints.
Adjacent angles are supplementary: The two angles that share a side add up to 180 degrees.

Examples of Parallelograms:
Rectangle: A parallelogram with four right angles.
Rhombus: A parallelogram with all sides equal in length.
Square: A parallelogram with both four right angles and all sides equal in length.