Mixed Content

Theorem 1: Parallelograms on same base and between same parallels are equal in area.Theorem 2: The area of a parallelogram is the product of its any side and the corresponding altitude.Theorem 3: Two triangles on the same base and between same parallels are equal in area.Theorem 4: The area of a triangle is half the product of any of the sides and the corresponding altitude.Q1. In the figure ABCD is a parallelogram. AM _|_ CD & CN _|_ AD. If AB = 12cm, AM = 8cm & CN = 9cm find AD.Q2. If P, Q, R, S are respectively the midpoints of the sides AB, BC, CD, DA of a parallelogram ABCD, show that area(PQRS) = ½ area (ABCD) .Q3. In the given figure, P is a point in the interior of a parallelogram ABCD. Show that (i) area (∆ APB) + area (∆ PCD) = ½ area (ABCD) (ii) area (∆ APD ) + area (∆ PBC) = area (∆ APB) + area ( ∆PCD).Q4. Show that the median of a triangle divides it into two triangle of equal area.Q5. In the ∆ ABC, E is the midpoint of median AD. Show that area (∆ BED) = ¼ area (∆ABC)Q6. Prove that the area of a Rhombus is equal to half the rectangle contained by its diagonals.H.WQ1. Prove that a parallelogram & a rectangle on the same base & between same parallels are equal in area.Q2. Prove that the diagonals of a parallelogram divide it into 2 ∆’s of equal area.Q3. Prove that the line segment joining the midpoints of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms.Q4. In the figure ABCD is a quadrilateral & DP || AC. Show that area (∆ ABP) = area (ABCD).Q5. Show that the diagonals of a parallelogram divide it into 4 triangles of equal.Q6. In the figure ABCD is a parallelogram whose diagonals AC & BD intersect at O.A line segment through O meets AB at E & DC at F. Prove that area ( AEFD ) = ½ area ( ABCD ).Q7. P & Q are any two points lying on the sides DC & AD respectively of a parallelogram ABCD. Show that Area ( ∆ APB ) = area (∆ BQC).Q8. In the figure ABCD is a parallelogram AB = 8cm, altitude AQ = 7cm, altitude AP = 4cm, find the perimeter of parallelogram ABCD. Q9. If each diagonal of a quadrilateral divides it into two triangles of equal area then show that the quadrilateral is a parallelogram.Q10. ABCD is rhombus I which AC & BD are its diagonals intersecting at .Prove that area (ABCD) = ½ AC x BD.