Quadrilateral Theorem 8.1 A diagonal of a parallelogram divides it into two congruent triangles.
Show that the diagonals of a rhombus are perpendicular to each other
If the diagonals of a parallelogram are equal, then show that it is a rectangle
Show that the diagonals of a square are equal and bisect each other at right angles
Diagonal AC of a parallelogram ABCD bisects A. Show that it bisects c also ABCD is a rhombus
ABCD is a rectangle in which diagonal AC bisects angle A as well as angle C Show that ABCD is a square
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see figure). Show that
In Δ ABC and Δ DEF, 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). Show that
ABCD is a trapezium in which AB is parallel to CD and AD = BC Show that
ABCD is a quadrilateral in which P, Q, R and S are midpoints of the sides AB, BC, CD and DA see Fig 8.29 AC is a diagonal Show that
ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
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
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. Show that F is the mid-point of BC.
In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.
Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other
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