prove that the diagonal of a rectangle are equal
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The diagonals of a rectangle are equal. Let ABCD be a rectangle. We prove that AC = BD. Hence AC = DB (matching sides of congruent triangles).
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1)The opposite angles of a parallelogram are equal.
2)The opposite sides of a parallelogram are equal.
3)The diagonals of a parallelogram bisect each other.( actual answer)
Step-by-step explanation:( just to know )
. Yes, the diagonals of a rectangle are equal. This is because the two diagonals are the hypotenuse of the two right angled triangles formed by the diagonals. Since, the height and base of the two triangles are equal, by Pythagoras Theorem, the hypotenuse of the triangles are also equal.
. Now, the congruent parts of two congruent triangles are equal. Therefore, we have proved that the diagonals of the rectangle are equal.
. Convex quadrilaterals
Euler diagram of some types of simple quadrilaterals. (UK) denotes British English and (US) denotes American English.
Convex quadrilaterals by symmetry, represented with a Has diagram.
In a convex quadrilateral all interior angles are less than 180°, and the two diagonals both lie inside the quadrilateral.
Irregular quadrilateral (British English) or trapezium (North American English): no sides are parallel. (In British English, this was once called a trapezoid. For more, see Trapezoid § Trapezium vs Trapezoid)
Trapezium (UK) or trapezoid (US): at least one pair of opposite sides are parallel. Trapezia (UK) and trapezoids (US) include parallelograms.
Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.
Parallelogram: a quadrilateral with two pairs of parallel sides. Equivalent conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other. Parallelograms include rhombi (including those rectangles called squares) and rhomboids (including those rectangles called oblongs). In other words, parallelograms include all rhombi and all rhomboids, and thus also include all rectangles.
Rhombus, rhomb:[2] all four sides are of equal length (equilateral). An equivalent condition is that the diagonals perpendicularly bisect each other. Informally: "a pushed-over square" (but strictly including a square, too).
Rhomboid: a parallelogram in which adjacent sides are of unequal lengths, and some angles are oblique (equiv., having no right angles). Informally: "a pushed-over oblong". Not all references agree, some define a rhomboid as a parallelogram that is not a rhombus.[4]
Rectangle: all four angles are right angles (equiangular). An equivalent condition is that the diagonals bisect each other, and are equal in length. Rectangles include squares and oblongs. Informally: "a box or oblong" (including a square).
Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), and that the diagonals perpendicularly bisect each other and are of equal length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle (i.e., four equal sides and four equal angles).
Oblong: longer than wide, or wider than long (i.e., a rectangle that is not a square).[5]
Kite: two pairs of adjacent sides are of equal length. This implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. It also implies that the diagonals are perpendicular. Kites include rhombi.
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