![]() Line AB intersects AD and BC at A and B respectively, such that We know that the sum of the angles of a quadrilateral is 360 o. Solution : In quadrilateral ABCD, we have Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D. ![]() Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Theorem : In a parallelogram, opposite angles are equal. Similarly, line AC intersects BC and AD at C and A such that Now, line AC intersects AB and DC at A and C, such that Given : Let ABCD be a quadrilateral in which AB = CD and BC = AD. Theorem : If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Diagonal AC divides parallelogram ABCD into two congruent triangles ABC and CDA. Similarly, AB || DC and AC is a transversal Given : ABCD is a parallelogram and AC be diagonal. Theorem : A diagonal of a parallelogram divides it into two congruent triangles. (v) A rectangle or a rhombus is not a square. (i) A square is a rectangle and also a rhombus VI A Kite : In a quadrilateral ABCD, if AD = CD and AB = CB, then it is called a kite i.e., two pairs of adjacent sides are equal but it is not a parallelogram. AB || CD, AD || BC, AB = BC = CD = DA and ∠A = ∠B = ∠C = ∠D = 90 o V A Square : In a quadrilateral (parallelogram) if all sides are equal and all angles are 90 o, then it is called a square. ![]() IV A Rhombus : In a quadrilaterals (parallelogram) if all sides are equal, then it is called a rhombus, i.e., AB || CD, AD || BC and AB = BC = CD = DA, then ABCD is a rhombus. AB || CD, AB = CD, AD || BC AD = BC and ∠A = ∠B = ∠C = ∠D = 90 o, then ABCD is a rectangle. A Rectangle : In a quadrilaterals (parallelogram) if all angles are right angles, then it is called a rectangle. i.e., AB || CD and AB = CD AD || BC and AD = BC, then ABCD is a parallelogram. A parallelogram : In a quadrilateral, if both pairs of opposite sides are parallel and equal, then it is called a parallelogram. If AB || CD then quadrilateral ABCD is a trapezium. A Trapezium : In a quadrilateral if one pair of opposite sides is parallel, then it is called a trapezium i.e. Given : Let ABCD be a quadrilateral and AC be its one diagonal Theorem : The sum of the angles of a quadrilateral is 360 o A quadrilateral has four sides, four angles, four vertices and two diagonals.ĩ.2. ![]() ABCD is a quadrilateral which has four sides AB, BC, CD and DA, four angles ∠ A, ∠ B, ∠ C and ∠ D and four vertices A, B, C and D and also has two diagonals AC and BD. We can say that a quadrilateral is a closed figure with four sides :Į.g. Hence the opposite side length is the same, we can use this also to prove that the quadrilateral that is formed with these points is a parallelogram.If there are four points in a plane in such a way that no three of them are collinear, then the figure obtained by joining four points, in order is called a quadrilateral. We know that, for any given two points, \ the slope of the line joining two points is \ respectively. We can prove that this is a parallelogram by showing that the slope of the opposite sides is the same. As we know that the opposite sides of a parallelogram are parallel, which means that their slope is the same. We have to prove that these points make a parallelogram.
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