The angles of a quadrilateral are in the ratio 3 : 5: 9: 13. Find all the angles of the quadrilateral.
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.
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.
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal
BD (see Fig. 8.21). Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ
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.
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
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