Quadrilaterals and Polygons
Three vertices of a parallelogram $$ABCD$$ are $$A (3, -1, 2), B(1, 2, -4)$$ and $$C (-1, 1, 2)$$. Find the coordinates of the fourth vertex.
Name each of the following parallelograms. (i) The diagonals are equal and the adjacent sides are unequal. (ii) The diagonals are equal and the adjacent sides are equal. (iii) The diagonals are unequal and the adjacent sides are equal.
$$(i)$$ The diagonals are equal and the adjacent sides are unequal.
$$\Rightarrow$$ Rectangle is the name of parallelogram which diagonal are equal and adjacent side are unequal.
$$(ii)$$ The diagonals are equal and the adjacent sides are equal.
$$\Rightarrow$$ Square is the name of parallelogram in which diagonals are equal and the adjacent sides are equal.
$$(iii)$$ The diagonals are unequal and the adjacent sides are equal.
$$\Rightarrow$$ Rhombus is the name of parallelogram in which diagonals are unequal and the adjacent sides are equal.
Three vertices of a parallelogram $$ABCD$$ are $$A (3, -1, 2), B(1, 2, -4)$$ and $$C (-1, 1, 2)$$. Find the coordinates of the fourth vertex.
The measures of two adjacent angles of a parallelogram are in the ratio $$3 : 2$$. Find the measure of each of the angles of the parallelogram.
The sum of two opposite angles of a parallelogram is $$130^o$$. Find the measure of each of its angles.
The measure of two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each angle of the parallelogram.
The perimeter of a parallelogram is 140 cm. If one of the sides is longer than the other by 10 cm,find the length of each of its sides.
$$ABCD$$ is a parallelogram in which $$\angle {110^{o}}.$$ Find the measure of each of angles $$\angle B,\ \angle C$$ and $$\angle D.$$
Two adjacent angles of a parallelogram are $$\left(2x+25\right)^{o}$$ and $$\left(3x-5\right)^{o}.$$ The value of $$x$$ is
The diagonals do not necessarily intersect at right angles in a
Two adjacent side of a parallelogram are 15 cm. If the distance between the longer sides is 8 cm , find the ares of the parallelogram. Also find the distance between shorter sides.
Show that the diagonals of a parallelogram divide it into four triangles of equal area.