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Diagonals of a Parallelogram

Write the ant...

Question

Write the antecedent (given part) and the consequent (part to be proved) in the following statements.

(i) If all sides of a triangle are congruent then its all angles are congruent.

(ii) The diagonals of a parallelogram bisect each other.

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Solution

(i) Antecedent : All the sides of a triangle are congruent.
Consequent : Its all angles are congruent.

(ii) The statement can be written in conditional form as, 'If the given quadrilateral is a parallelogram, then its diagonals bisect each other.
Antecedent : The given quadrilateral is a parallelogram.
Consequent : Its diagonals bisect each other.

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Similar questions

Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent.

(i) Two equilateral triangles are similar.

(ii) If angles in a linear pair are congruent then each of them is a right angle.

(iii) If the altitudes drawn on two sides of a triangle are congruent then those two sides are congruent.

Q. The antecedent of the conditional statement "If all sides of a triangle are congruent then its all angles are congruent" is :

Q. Which of the quadrilaterals mentioned in brackets have the following properties?

(1) Diagonals are congruent. (square, rectangle, rhombus)
(2) The longer diagonal is the perpendicular bisector of the shorter and the shorter of the longer. (trapezium, kite, rhombus)
(3) All sides and angles are congruent. (rhombus, square, rectangle)
(4) Opposite angles are congruent. (kite, parallelogram, rectangle)
(5) Opposite sides are congruent. (trapezium, rectangle, parallelogram)
(6) Diagonals bisect each other at right angles. (square, rectangle, rhombus)
(7) Diagonals bisect each another. (rectangle, parallelogram, kite)
(8) One pair of opposite sides is parallel. (kite rhombus trapezium)

Write the following statements in ‘if-then’ form.

(i) The opposite angles of a parallelogram are congruent.

(ii) The diagonals of a rectangle are congruent.

(iii) In an isosceles triangle, the segment joining the vertex and the mid point of the base is perpendicular to the base.

Which of the following statements are true (T) and which are false (F) ?

(i) In a parallelogram, the diagonals are equal.

(ii) In a parallelogram, the diagonals bisect each other.

(iii) In a parallelogram, the diagonals bisect each other at right angles.

(iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.

(v) If all the angles of a quadrilateral are equal, it is a parallelogram.

(vi) If three sides of a quadrilateral are equal, it is a parallelogram.

(vii) If three angles of a quadrilateral are equal, it is a parallelogram

(viii) If all the sides of a quadrilateral are equal it is a parallelogram.

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Diagonals of a Parallelogram

Standard VIII Mathematics

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