exercise - 8.1 🔥|Part - 2 | Quadrilaterals😍| Chapter - 8 |

exercise - 8.1 🔥|Part - 2 | Quadrilaterals😍| Chapter - 8 | #quadrilateralsclass9 #class9thmaths




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diagonals of a rectangle bisect each other and are equal and vice-versa,
diagonals of a rhombus bisect each other at right angles and vice-versa,
diagonals of a square bisect each other at right angles and are equal, and vice-versa,
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,
a line through the mid-point of a side of a triangle parallel to another side bisects the third side,
mid point theorem,
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4. ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that:
(i) ABCD is a square
(ii) diagonal BD bisects ∠ B as well as ∠ D.




5. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig.). Show that:
(i) ∆ APD ≅ ∆ CQB
(ii) AP = CQ
(iii) ∆ AQB ≅ ∆ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram




6. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig.). Show that
(i) ∆ APB ≅ ∆ CQD
(ii) AP = CQ




7. ABCD is a trapezium in which AB || CD and AD = BC (see Fig.). Show that
(i) ∠ A = ∠ B
(ii) ∠ C = ∠ D
(iii) ∆ ABC ≅ ∆ BAD
(iv) diagonal AC = diagonal BD
[Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]





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.