Free Understanding Quadrilaterals 01 Practice Test - 8th Grade
A polygon comes under which of the following categories?
Solution : A and B
The polygon is a simple closed curve made up of line segments. Each line segment represents a side of a polygon.
The polygon is also a plane figure with atleast three sides and three angles.
The sum of exterior angles of a polygon (in degrees) with 10 sides is
Solution : The sum of all exterior angles of a polygon, irrespective of the number of its sides, is equal to 360∘. If the polygon is regular, the measure of each exterior angle can be calculated by dividing 360∘ by the total number of sides in the polygon.
A quadrilateral has two of its angles as 30∘ and 40∘. What type of quadrilateral can it be?
Solution : A
In square and rectangle each angle is 900.
In a parallelogram, two adjacent angles have to be either equal or supplementary. The angles 30∘ and 40∘ are neither supplementary nor equal. So, the two angles cannot belong to a parallelogram.
For trapezium, there are no such restrictions. So, the given qudrilateral is a trapezium.
A square is also a
Solution : A, B, and C
A square is a parallelogram because it has opposite pairs of sides parallel and equal.
It is also a rhombus because it has all its sides equal, opposite sides are parallel and the diagonals intersect at 90∘.
A square is also a rectangle because all its angles are 90∘ and its pair of opposite sides are equal and parallel.
A square can't be a trapezium as in trapezium only one of the opposite sides are parallel.
Consider the figure shown. What type of quadrilateral can it be?
Solution : B
In the given figure the pair of opposite sides are parallel and equal. So, the given figure is a parallelogram.
Among the options, the quadrilateral ABCD can be either 'Rhombus' or 'Parallelogram'. [∵ Rhombus is also a parallelogram]
But adajcent sides of ABCD are not equal (ie, AD and CD are not equal).
So, ABCD cannot be a rhombus. Hence, ABCD is a paralleogram.
The number of sides in a kite is
A kite is a quadrilateral. Hence it has 4 sides.
I draw a quadrilateral and then draw all its diagonals.How many triangles can I find?
Solution : C
The triangles are-
⟹There are 8 triangles in the figure.
In parallelogram ABCD, which of the two angles are equal?
Solution : C
In a parallelogram, the two opposite angles are equal. Hence, if the four vertices of a parallelogram are A, B, C, D in cyclic order, then ∠A & ∠C and ∠B & ∠D are equal.
In parallelogram ABCD, which of the 2 sides are equal?
Solution : D
The opposite sides of a parallelogram are equal.
Hence, sides AB & CD (if the cyclic order of the vertices are A, B, C, D) are opposite sides and are equal.
There is a pair of parallel lines which intersects with another pair of parallel lines. The quadrilateral formed is trapezium.
Solution : B
The quadrilateral formed between two pairs of parallel lines is a parallelogram. In a trapezium, the only one pair of opposite sides is parallel.