Quadrilaterals

Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

Reliable Education Group April 25, 2022

Quadrilaterals

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD.

Reliable Education Group April 25, 2022

Quadrilaterals

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

Reliable Education Group April 25, 2022

Quadrilaterals

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.

Reliable Education Group April 25, 2022

Quadrilaterals

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. 8.30). Show that F is the mid-point of BC.

Reliable Education Group April 25, 2022

Quadrilaterals

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that:

Reliable Education Group April 25, 2022

Quadrilaterals

In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22).

Reliable Education Group April 25, 2022

Quadrilaterals

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

Reliable Education Group April 25, 2022

Quadrilaterals

ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that

Reliable Education Group April 25, 2022

Quadrilaterals

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that:

Reliable Education Group April 25, 2022

Quadrilaterals

Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig. 8.19). Show that

Reliable Education Group April 25, 2022

Quadrilaterals

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that

Reliable Education Group April 25, 2022

Quadrilaterals

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:

Reliable Education Group April 25, 2022

Quadrilaterals

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square

Reliable Education Group April 25, 2022

Quadrilaterals

Show that the diagonals of a square are equal and bisect each other at right angles.

Reliable Education Group April 25, 2022

Quadrilaterals

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Reliable Education Group April 25, 2022

Quadrilaterals

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Reliable Education Group April 25, 2022