![]() So |AO|=|OC|, and we have our second side for the Side-Angle-Side postulate.Īnd if triangles ΔAOD and ΔCOD are congruent, |AD|=|DC|, and we are done showing that a parallelogram with perpendicular diagonals is a rhombus. If one side of the cyclic quadrilateral is produced, then the exterior angle. So let's review the properties of parallelograms - one of them is that the diagonals bisect each other. Also, the consecutive angles of a parallelogram are supplementary. We now need either another side, or another angle to show the triangles are congruent. We know that the opposite angles of a parallelogram are equal. We have one common side - OD, and since the diagonals are perpendicular, m∠AOD = m∠COD=90°, and so ∠AOD ≅ ∠COD. And to do that, we just have to realize that we have. So for example, we want to prove that CAB is congruent to BDC, so that that angle is equal to that angle, and that ABD, which is this angle, is congruent to DCA, which is this angle over here. We will do this using congruent triangles. What I want to do in this video is prove that the opposite angles of a parallelogram are congruent. So we need to show that one pair of adjacent sides is equal. Given sides of parallelogram A ( 2, 1), B (a, 0), C (4, b), D (1, 2) We know that diagonals of Parallelogram bisect each other. We know that the opposite sides in ABCD are equal, because it is a parallelogram. StrategyĪBCD is a rhombus if all its sides are equal. Click on the button below to turn the pure parallel lines into a parallelogram. ProblemĪBCD is a parallelogram, and its diagonals are perpendicular - AC⊥DB. Here we will show the converse- that if a parallelogram has perpendicular diagonals, it is a rhombus - all its sides are equal. The Sum of adjacent angles of a parallelogram is equal to 180 degrees. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. We've seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other. Maths Math Article Parallelogram Parallelogram A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. A rhombus is a special kind of parallelogram, in which all the sides are equal.
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