For StudentsFor ParentsFor SchoolsSuccess StoriesOutcomesAI MATHEMATICS>Quadrilaterals>MULTIPLE CHOICE QUESTIONS>Q 17 50% students answered this correctly Learn the theorems on quadrilaterals, such as properties related to the diagonal of a parallelogram and the opposite sides and angles of a parallelogram etc. A parallelogram could also be called a trapezoid as it has two parallel sides. But do we also know that a parallelogram is a convex quadrilateral? Watch the... We now know that in a parallelogram, opposite sides are parallel and equal in length. In this video, we will study the elements and properties of a parallelo... Have you noticed a TV, an envelope or a kite? They all have a similar shape. Such a shape is called a quadrilateral. Let’s learn more about the types of quad... Songs! You love them, don't you? Let's groove with the beats of this song and learn more about the properties of a parallelogram! Are you ready? The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is a rectangle. Explanation: The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side. Join AC, RP and SQ In ∆ABC, P is midpoint of AB and Q is midpoint of BC ∴ By midpoint theorem, PQ ∥ AC and PQ = `1/2`AC ......(1) Similarly, In ∆DAC, S is midpoint of AD and R is midpoint of CD ∴ By midpoint theorem, SR ∥ AC and SR = `1/2`AC ......(2) From (1) and (2), PQ ∥ SR and PQ = SR ⇒ PQRS is a parallelogram ABQS is a parallelogram ⇒ AB = SQ PBCR is a parallelogram ⇒ BC = PR ⇒ AB = PR ......[∵ BC = AB, sides of rhombus] ⇒ SQ = PR ∴ Diagonals of the parallelogram are equal. |