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. So let's review the properties of parallelograms - one of them is that the diagonals bisect each other. We now need either another side, or another angle to show the triangles are congruent. We have one common side - OD, and since the diagonals are perpendicular, m∠AOD = m∠COD=90°, and so ∠AOD ≅ ∠COD. We will do this using congruent triangles. Which statement explains how you could use coordinate geometry to prove that quadrilateral abcd is a square shape abcd is shown. In Figure 4, AC is a diagonal of parallelogram ABCD.

To discover its properties, we will draw a diagonal, a line connecting the opposite vertices of the parallelogram. So we need to show that one pair of adjacent sides is equal. A parallelogram is a quadrilateral in which the opposite sides are parallel (Figure 3.1.3 ). Note- In this particular problem, in order to prove that the parallelogram is a rhombus we have to prove that all the sides of the parallelogram circumscribing the circle will be equal. 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. ProblemĪBCD is a parallelogram, and its diagonals are perpendicular - AC⊥DB. (ii) The bisectors of the opposite angles are parallel to each other. Here we will show the converse- that if a parallelogram has perpendicular diagonals, it is a rhombus - all its sides are equal. In case of a parallelogram prove that: (i) The bisectors of any two adjacent angles intersect at 90 o.

We've seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other. In the Given Figure, Abcd is a Parallelogram, P and Q Are Midpoints of Side Ab and Dc Respectively, Then Prove Apcq is a Parallelogram. A vertical stick 20 cm long casts a shadow 6 cm long on the ground. In an isosceles ABC, the base AB is produced both ways in P and Q such that AP × BQ AC 2 and CE are the altitudes. In figure, if A C, then prove that AOB COD. A rhombus is a special kind of parallelogram, in which all the sides are equal. Prove that: 'AP'/'BP''AQ'/'QC' In figure, find L.

Prove that abcd is a parallelogram