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What is the negation of the statement quadrilateral abcd is a paralleogram and it has a right angle?
"abcd is not a parallelogram or it does not have any right angles." ~(P and Q) = ~P or ~Q
What is the area of the quadrilateral ABCD whose vertices are at -1 4 and 3 7 and 5 2 and -5 -17 giving the reason for your answer?
When the given vertices are plotted and joined together on the Cartesian plane they will form a 4 sided quadrilateral whose diagonals intercept each other at right angles and so multiplying the lengths of the diagonals divided by two will produce an area of 80 square units.
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.
When can this be true abcd is a quadrilateral does a plus b plus c plus d equals 180?
No; it is false. The sum of all the angles of a quadrilateral always equals 360o.
What is the area of the quadrilateral ABCD whose vertices are at -1 4 and 3 7 and 5 2 and -4 -17 respectively on the Cartesian plane?
Its diagonals intersect each other at right angles when plotted on the Cartesian plane Its diagonal lengths are 2 times square root of 10 and 8 times square root of 10 Its area is 0.5 times product of its diagonals equals 80 square units
