Maths

5. P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC = BD and AC ⊥ BD. Prove that PQRS is a square. -q 5. P BC CD and DA of quadrilateral ABCD in which AC = BD and AC ⊥ BD. Prove [...]

4. P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC ⊥ BD. Prove that PQRS is a rectangle. -q 4. P BC CD and DA of a quadrilateral ABCD such that AC ⊥ BD. Prove that PQRS is a rectangle. [...]

3. P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus. -q 3. P BC CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus. [...]

2. In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF. 2. In a parallelogram ABCD AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in [...]

1. A square is inscribed in an isosceles right triangle so that the square and the triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse. 4. ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the [...]

10. In Fig. 8.7, P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. Prove that AD = 2CD. 10. In Fig. 8.7 P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. Prove that AD = 2CD. July 1, 2021 Category: Chapter [...]

9. Points P and Q have been taken on opposite sides AB and CD, respectively of a parallelogram ABCD such that AP = CQ (Fig. 8.6). Show that AC and PQ bisect each other. 9. Points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that [...]

8. D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral triangle ABC. Show that ∆ DEF is also an equilateral triangle. 8. D CA and AB E and F are the mid-points of the sides BC respectively of an equilateral triangle ABC. Show that ∆ DEF [...]

7. Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a ∆ ABC as shown in Fig.8.5. Show that BC = 1/2 QR. 7. Through A b and c`. CA and AB of a ∆ ABC as shown in Fig.8.5. Show that [...]

6. E is the mid-point of the side AD of the trapezium ABCD with AB || DC. A line through E drawn parallel to AB intersect BC at F. Show that F is the mid-point of BC. [Hint: Join AC] 6. E is the mid-point of the side AD of the trapezium ABCD with AB [...]