In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that
MN bisects QS.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
ABCD is a trapezium in which side AB is parallel to side DC. P is the mid-point of side AD. IF Q is a point on the Side BC such that the segment PQ is parallel to DC, prove that PQ = `(1)/(2)("AB" + "DC")`.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In the given figure, PQRS is a parallelogram in which PA = AB = Prove that: SA ‖ QB and SA = QB.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In the given figure, PQRS is a parallelogram in which PA = AB = Prove that: SAQB is a parallelogram.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In the given figure, PQRS is a trapezium in which PQ ‖ SR and PS = QR. Prove that: ∠PSR = ∠QRS and ∠SPQ = ∠RQP
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
Prove that the diagonals of a kite intersect each other at right angles.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
Prove that the diagonals of a square are equal and perpendicular to each other.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
Observe the given frequency table to answer the following:
| Class Interval |
20 - 24 |
25 29 |
30 - 34 |
35 - 39 |
40 - 44 |
45 - 49 |
| Frequency |
6 |
12 |
10 |
15 |
9 |
2 |
a. The true class limits of the fifth class.
b. The size of the second class.
c. The class boundaries of the fourth class.
d. The upper and lower limits of the sixth class.
e. The class mark of the third class.
[18] Statistics
Chapter: [18] Statistics
Concept: undefined >> undefined
Construct a rhombus ABCD, given AB = 3.8cm and ∠A = 60°. Measure AC.
[15] Construction of Polygons (Using Ruler and Compass Only)
Chapter: [15] Construction of Polygons (Using Ruler and Compass Only)
Concept: undefined >> undefined
Construct a rhombus whose perimeter is 16cm and BD = 6.2cm.
[15] Construction of Polygons (Using Ruler and Compass Only)
Chapter: [15] Construction of Polygons (Using Ruler and Compass Only)
Concept: undefined >> undefined
Construct a rhombus whose diagonals AC = 7.4cm and BD = 6cm.
[15] Construction of Polygons (Using Ruler and Compass Only)
Chapter: [15] Construction of Polygons (Using Ruler and Compass Only)
Concept: undefined >> undefined
Construct a rhombus whose side AB = 5cm and diagonal AC = 6cm. MEasure DB and AD.
[15] Construction of Polygons (Using Ruler and Compass Only)
Chapter: [15] Construction of Polygons (Using Ruler and Compass Only)
Concept: undefined >> undefined
Prove that the diagonals of a parallelogram divide it into four triangles of equal area.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
The diagonals AC and BC of a quadrilateral ABCD intersect at O. Prove that if BO = OD, then areas of ΔABC an ΔADC area equal.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
PQRS is a parallelogram and O is any point in its interior. Prove that: area(ΔPOQ) + area(ΔROS) - area(ΔQOR) + area(ΔSOP) = `(1)/(2)`area(|| gm PQRS)
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In the given figure, AB ∥ SQ ∥ DC and AD ∥ PR ∥ BC. If the area of quadrilateral ABCD is 24 square units, find the area of quadrilateral PQRS.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In the given figure, PQ ∥ SR ∥ MN, PS ∥ QM and SM ∥ PN. Prove that: ar. (SMNT) = ar. (PQRS).
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In ΔABC, the mid-points of AB, BC and AC are P, Q and R respectively. Prove that BQRP is a parallelogram and that its area is half of ΔABC.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In ΔPQR, PS is a median. T is the mid-point of SR and M is the mid-point of PT. Prove that: ΔPMR = `(1)/(8)Δ"PQR"`.
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
In the figure, ABCD is a parallelogram and CP is parallel to DB. Prove that: Area of OBPC = `(3)/(4)"area of ABCD"`
[14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter: [14] Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Concept: undefined >> undefined
