exercise - 8.2 🔥| mid - point theorem 😍| Quadrilaterals🔥| Chapter - 8 |

exercise - 8.2 🔥| mid - point theorem 😍| Quadrilaterals🔥| Chapter - 8 | #quadrilaterals #class9th




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the line-segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it,
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3. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.




4. ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig.). Show that F is the mid-point of BC.




5. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig.). Show that the line segments AF and EC trisect the diagonal BD.




6. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i) D is the mid-point of AC
(ii) MD ⊥ AC
(iii) CM = MA = 1/2 AB





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.