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Quadrilaterals: Practice 3

Section A: Core Practice

Question 1mcq
A student says, 'If a parallelogram has equal diagonals, it must be a rectangle.' Which statement is best?
A.It must be a rhombus only.
B.Equal diagonals prove all four sides are unequal.
C.It cannot be a parallelogram.
D.A rectangle is enough to guarantee equal diagonals.
Question 2mcq
Which quadrilateral is usually defined as having one pair of opposite sides parallel?
A.A trapezium
B.Rhombus
C.Square
D.Kite
Question 3mcq
Which angle property is true for every parallelogram?
A.Adjacent angles are equal.
B.All angles are 90∘90^\circ.
C.Each angle is 60∘60^\circ.
D.Both pairs of opposite angles are equal.
Question 4mcq
A rough sketch of a quadrilateral looks like a rectangle, but only opposite sides are given parallel. Can we conclude it is a rectangle?
A.No quadrilateral can have opposite sides parallel.
B.Yes, every parallelogram is a rectangle.
C.Yes, every quadrilateral with parallel sides is a square.
D.No, because the diagram may show a special case but the given conditions do not force it.
Question 5mcq
Which description best identifies a parallelogram?
A.Any polygon with four or more sides
B.A quadrilateral with two pairs of opposite sides parallel
C.A quadrilateral with exactly one pair of parallel sides
D.A four-sided figure with all angles unequal
Question 6mcq
Three angles of a quadrilateral are 75∘75^\circ, 105∘105^\circ, and 65∘65^\circ. What is the fourth angle?
A.125∘125^\circ
B.65∘65^\circ
C.105∘105^\circ
D.115∘115^\circ

Section B: Reasoning and Application

Question 7mcq
Which property is always true for a parallelogram?
A.All four angles are right angles.
B.Diagonals are always equal and perpendicular.
C.Opposite sides are equal and parallel.
D.All four sides are equal.
Question 8mcq
Which quadrilateral has all sides equal and all angles right angles?
A.A general parallelogram
B.A kite
C.A trapezium
D.A square
Question 9mcq
A student says, 'If a parallelogram has equal diagonals, it must be a rectangle.' Which statement is best?
A.A rectangle is enough to guarantee equal diagonals.
B.Equal diagonals prove all four sides are unequal.
C.It must be a rhombus only.
D.It cannot be a parallelogram.
Question 10mcq
Which quadrilateral is usually defined as having one pair of opposite sides parallel?
A.Rhombus
B.Square
C.A trapezium
D.Kite
Question 11mcq
Which angle property is true for every parallelogram?
A.Both pairs of opposite angles are equal.
B.Each angle is 60∘60^\circ.
C.Adjacent angles are equal.
D.All angles are 90∘90^\circ.
Question 12mcq
A rough sketch of a quadrilateral looks like a rectangle, but only opposite sides are given parallel. Can we conclude it is a rectangle?
A.Yes, every parallelogram is a rectangle.
B.No quadrilateral can have opposite sides parallel.
C.No, because the diagram may show a special case but the given conditions do not force it.
D.Yes, every quadrilateral with parallel sides is a square.