Mathematics
Assertion (A) : If diagonals of a quadrilateral are equal, then it must be a rectangle.
Reason (R) : The diagonals of a rectangle are equal.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Rectilinear Figures
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Answer
For a quadrilateral to be a rectangle, the diagonals must be equal and they must bisect each other.Having equal diagonals is not enough to say a quadrilateral to be a rectangle.
Assertion (A) is false.
This is a fundamental property of rectangles.
If we have a rectangle ABCD, we can prove the diagonals AC and BD are equal using the SAS congruence rule on △ABC and △DCB.
AB = DC (Opposite sides)
∠B = ∠C = 90°
BC = BC (Common side)
Therefore, AC = BD.
Reason (R) is true.
A is false, R is true
Hence, option 2 is the correct option.
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Related Questions
Rajbeer is a farmer. He has a plot of land in the shape of a quadrilateral ABCD as shown in the figure. In ABCD, AB ∥ CD and AD ∥ BC. He divided the field into two parts, viz, triangle BCE and trapezium CDAE by making an embankment CE such that CE = AD.
Based on the above information, answer the following questions :
1. ABCD is a :
(a) Rectangle
(b) Parallelogram
(c) Square
(d) Trapezium2. ∠A is equal to :
(a) ∠D
(b) ∠B
(c) ∠C
(d) ∠E3. ∠DCE is equal to :
(a) ∠E
(b) ∠A
(c) ∠D
(d) ∠B4. Which of the following is correct?
(a) ΔAEC ≅ ΔEAD
(b) ΔACE ≅ ΔAED
(c) ΔCEA ≅ ΔEAD
(d) none of these5. Diagonal DE is equal to :
(a) diagonal DB
(b) diagonal AC
(c) DC
(d) BCAssertion (A) : The two diagonals of a rectangle are equal and bisect each other at right angles.
Reason (R) : Every rectangle is a square.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A) : Every square is a parallelogram.
Reason (R) : In a square as well as in a parallelogram, the diagonals are equal in length.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
If bisectors of ∠A and ∠B of a parallelogram ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a :
rectangle
rhombus
parallelogram
quadrilateral whose opposite angles are supplementary