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.
$$ABCD$$ is a parallelogram in which $$\angle {110^{o}}.$$ Find the measure of each of angles $$\angle B,\ \angle C$$ and $$\angle D.$$
Given $$\angle {110^{o}}.$$
But we know that sum of adjacent angles of a parallelogram is $$180^o$$
$$\angle A+ \angle B=180^o$$
$$\angle B=180^O-110^O=70^O$$
Also $$\angle B +\angle C=180^o$$ [Since $$\angle B$$ and $$\angle C$$ are adjacent angles]
$$70^o+\angle C=180^o$$
$$\angle C=180^o-70^o=110^o$$
Now, $$\angle C+\angle D=180^o$$ [Since $$\angle C$$ and $$\angle D$$ are adjacent angles]
$$110^o + \angle D=180^o$$
$$\angle D=180^o-110^o=70^o$$
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.
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.
(a) In the figure ( 1 ) given below, the perimeter of parallelogram is $$ 42 \mathrm{cm} $$. Calculate the lengths of the sides of the parallelogram.