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.

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Solution

(i) If a quadrilateral is a parallelogram, then the opposite angles of that quadrilateral are congruent.
(ii) If a quadrilateral is a rectangle, then the diagonals are congruent.
(iii) If a triangle is an isosceles triangle, then segment joining the vertex of a triangle and midpoint of the base is perpendicular to the base.

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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.

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.

Write converses of the following statements.

(i) The alternate angles formed by two parallel lines and their transversal are congruent.

(ii) If a pair of the interior angles made by a transversal of two lines are supplementary then the lines are parallel.

(iii) The diagonals of a rectangle are congruent.

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)

State, true or false :
(i) Two similar polygons are necessarily congruent.
(ii) Two congruent polygons are necessarily similar.
(iii) All equiangular triangles are similar.
(iv) All isosceles triangles are similar.
(v) Two isosceles-right triangles are similar.
(vi) Two isosceles triangles are similar if an angle of one is congruent to the corresponding angle of the other.
(vii) The diagonals of a trapezium divide each other into proportional segments.

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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.

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.