geometry rectangle construction one side and diagonal

Diagonal and the angle included by them are given. A Rectangle ABCD, given AC = 7cm, BC = 7 cm and the angle included by them is 60 o . (i) Draw AC = 7 cm. (ii) Construct its perpendicular bisector to obtain the midpoint O. (iii) At O, construct CO..

. The diagonals bisect the angles of the rhombus. If the diagonals of a parallelogram are at right angles, it is a rhombus. Some special constructions: 1. Construction of Parallelograms when (a) Two sides and an angle are given (b) Diagonals..

AC = 5.2 cm In a square diagonals are equal. (i) Draw AC = 5.2 cm. (ii) Construct XY which bisects AC at O. (iii) With centre O and radius 2.6 cm ((= BD), cut XY at D and B. (iv) Join AB, BC, CD and AD. (v) \ ABCD is the required square...

AB=AD (sides of a square are equal) AB||DC (opposite sides of a square are parallel) ABCD is parallelogram with consecutive sides equal. ABCD is a rhombus. (by definition) Since the diagonals of a rhombus are perpendicular to each other, AC ^ BD. ABCD is a parallelogram. ABCD is a re..

i) AD is the median i.e., BD = DC In D ABK, F is the mid-point of AB . (given) G is the mid-point of AK. (by construction) FG || BK or GC || BK ...(1) By theorem on line joining the mid-points of any two sides of a triangle. Similarly in D ACK, GE || CK or GB || CK From (..

The area of a parallelogram is equal to that of a rectangle of the same base and of the same altitude. ABCD is a parallelogram and ABEF is a rectangle. They have common base AB and same height AF (or BE) Corollary Parallelograms having equal bases and equal altitudes are equal i..

Parallelogram is a quadrilateral whose opposite sides are parallel and equal. A rectangle, a rhombus and a square are considered as parallelograms. A trapezoid is quadrilateral with exactly one pair of opposite sides being parallel. Hence, it is not a parallelogram. You have lea..

Question: The diagonals of a quadrilateral ABCD are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides is a rectangle. Answer: Given: . To prove: PQRS is a rectangle. Proof: SR||PQ and SR=PQ (since both SR and..

Question 1 - Question: Prove that the area of a trapezium is half the product of its height and the sum of the parallel sides. Answer: Given: ABCD is a trapezium in which AB || DC. Let AB = a, DC = b and CE = AF = h. To prove: Construction: Join AC. Proof: AC is the diagona..

Constructions are to be drawn by using ruler and compass only. It must be stressed that not all constructions are possible using a compass and straight edge alon..