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What are the properties of the diagonals of a rectangle?
A Rectangle is a quadrilateral (four sided polygon) with two pairs of equal and parallel sides (opposite sides are parallel and equal, one pair is usually a different length from the other pair but if they are equal it is called a square), and all angles are right angles (90°). It has two diagonals which have the properties:The diagonals are always congruent (of equal length);The diagonals bisect each other (cut each other into two equal parts);The diagonals do not bisect the angles (unless the rectangle is a square when they do);The diagonals are not perpendicular (unless the rectangle is a square when they do).PROOF of the diagonals congruent:Take a rectangle ABCD with diagonals AC and BD.Using Pythagoras on the triangles ACD and BCD:AC² = AD² + CD²BD² = BC² + CD²But as ABCD is a rectangle AD = BC since they are opposite and parallel; thus:AC² = AD² + CD² = BC² + CD² = BD²Thus, as AC and BD are the diagonals, they are equal.Therefore the diagonals of a rectangle are congruent.
The length of the rectangle is 7cm more than the widthThe perimeter is 78cm Find the rectangle?
The rectangle is 23cm x 16cmHalf the perimeter is 78 / 2= 39cm (which is one side and one end).39 - 7 = 32cm32 / 2 = 16cm (one end)16 + 7 = 23cm (one side)Proof:(23 + 16) x 2 = 78cm the perimeter.
Proof kite diagonal bisector conjecture?
The diagonals of a kite are perpendicular and therefore bisect each other at 90 degrees
Are the diagonals of a square are never perpendicular?
The diagonals of a square are always perpendicular. Proof: Without loss of generality, assume the square has side length 1 and one vertex is at the origin. The square ABCD is given by: A = (0,0) , B = (1,0) , C = (1,1) , D = (0,1) The diagonals are d1=AC and d2=BD. Finding equations for each of them yields d1 = x d2 = 1-x (you can double check this) So, the relative slopes are 1 and -1. Since their product is -1, they are perpendicular.
If the Perimeter of the rectangle is 38 inches the length is 3 inches more find the width?
The formula for the perimeter of a rectangle is P=2(l + w). You know that the length is 3" more than the width. Hence you could substitute x for the width and x+3 for the length and use the formula to solve for the width: P = 2(l + w) 38 = 2(x + 3 + x) 38 = 4x + 6 32 = 4x 8 = x Hence, the width is 8" and the length is 11" Proof: P = 2(11 + 8) P = 2(19) P = 38
