Maths 1 Marks Question

True. Solution: As a rectangle satisfies all the properties of a trapezium. So, we can say that, every rectangle is a trapezium but vice-versa is not true.

Adjacent angles of a parallelogram are supplementary. Solution: By property of a parallelogram, we know that, the adjacent angles of a parallelogram are supplementary.

False. Solution: As diagonals of a rhombus are perpendicular to each other but not equal.

If all sides of a quadrilateral are equal, it is a rhombus or square.
Solution:
As in both the quadrilaterals all sides are of equal length.

True. Solution: As a square has all the properties of a trapezium. So, we can say that, every square is a trapezium but vice-versa is not true.

A rectangle whose adjacent sides are equal becomes a square. Solution: If in a rectangle, adjacent sides are equal, then it is called a square.

True. Solution: It is the property of a parallelogram.

True. Solution: A rhombus can be constructed uniquely, if both diagonals are given.

A polygon is a simple closed curve made up of only line segments. Solution: since a simple closed curve made up of only line segments is called a polygon.

False. Solution: As we require at least five measurements to determine a quadrilateral uniquely.

The number of diagonals in a hexagon is equilateral triangle. Solution: as polygon is regular, i.e. length of each side is same.

Square is a regular quadrilateral. Solution: Since in square, all the sides are of equal length and all angles are equal.

True. Solution: A quadrilateral has two diagonals.

False. Solution: As all angles of a trapezium are not equal.

False. Solution: As its all sides are not equal.

Diagonals of a rectangle are equal. Solution: We know that, in a rectangle, both the diagonals are of equal length.

In a rhombus diagonals intersect at right angles.solution:
The diagonals of a rhombus intersect at right angles.

True. Solution: A quadrilateral can be drawn, if three sides and two diagonals are given.

True.
Solution:
Since a rhombus satisfies all the properties of a trapezium. So, we can say that, every rhombus is a trapezium but vice-versa is not true.

A quadrilateral in which a pair of opposite sides is parallel is trapezium.
Solution:
We know that, in a trapezium, one pair of sides is parallel.

True. Solution: We can draw a unique parallelogram, if both diagonals and the angle between them is given.

If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as kite.
Solution:
This is a property of kite, i.e., only one diagonal bisects the other.

True. Solution: The diagonals of a rectangle are equal.

False. Solution: Kite is not a parallelogram as its opposite sides are not equal and parallel.

True. Solution: If opposite angles are equal, it has to be a parallelogram.

A regular polygon is a polygon whose all sides are equal and all angles In a regular polygon, are equal. Solution: all sides are equal and all angles are equal.

False. Solution: Since in a trapezium, only one pair of sides is parallel.

False.
Solution:
We cannot draw a unique-quadrilateral, if four angles and one side is known.

False.
Solution:
As in a rhombus, each angle is not a right angle, so rhombuses are not squares.

The name of three-sided regular polygon is equilateral triangle. Solution: as polygon is regular, i.e. length of each side is same.

True.
Solution:
Every square is also a parallelogram as it has all the properties of a parallelogram but vice-versa is not true.

True. Solution: If diagonals are equal, then it is definitely a rectangle.

False.
Solution:
Because it is not a simple closed curve as it intersects with itself more than once.

False. Solution: Diagonals of a rectangle does not bisect each other.

False. Solution: As in a parallelogram, all angles are not right angles, while in a rectangle, all angles are equal and are right angles.

A rhombus is a parallelogram in which all sides are equal. Solution: As length of each side is same in a rhombus.

False.
Solution:
By definition of a regular polygon, we know that, a polygon is regular, if all sides and all angles are equal.

True.
Solution:
As a square possesses all the properties of a rhombus. So, we can say that, every square is a rhombus but vice-versa is not true.

True. Solution: A quadrilateral can be drawn, if all four sides and one angle is known.

A diagonal of a quadrilateral is a line segment that joins two opposite vertices of the quadrilateral. Solution: Since the line segment connecting two opposite vertices is called diagonal.

False Solution: A kite is a convex quadrilateral as the line segment joining any two opposite vertices inside it, lies completely inside it.

False. Solution: Since in a rectangle, opposite sides are equal and parallel but in a trapezium, it is not so.

If one diagonal of a rectangle is 6cm long, length of the other diagonal is square. Solution: If in a rectangle, adjacent sides are equal, then it is called a square.

True. Solution: Since rectangles satisfy all “the” “properties” of parallelograms. Therefore, we can say that, all rectangles are parallelograms but vice-versa is not true.

A quadrilateral can be constructed uniquely if its three sides and two included angles are given. Solution: We cap determine a quadrilateral uniquely, if three sides and two included angles are given.

True. Solution: We can construct a unique quadrilateral with given three angles given and two included sides.

No, it cannot be a rectangle, as in rectangle, both the diagonals are of equal lengths.

True. Solution: Since squares possess all the properties of rectangles. Therefore, we can say that, all squares are rectangles but vice-versa is not true.

True.
Solution:
A quadrilateral can be constructed uniquely, if four sides and one diagonal is known.

A quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure is kite. Solution: By the property of a kite, we know that, it has two opposite angles of equal measure.

If the diagonals of a quadrilateral bisect each other, it is a parallelogram. Solution: Since in a parallelogram, the diagonals bisect each other.