Question

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.

Answer 1

(i) The given statement can be written in conditional form as, ' If the given two traingles are equilateral, then they are similar.'
Antecedent : The given two triangles are equilateral.
Consequent : They are similar.

Here, ∆ABC and ∆PQR are equilateral triangles, so they are similar to each other.

(ii) Antecedent : The angles in a linear pair are congruent.
Consequent : Each of them is a right angle.

Here, ∠AOC and ∠BOC forming a linear pair are congruent to each other, so each of them is a right angle.

(iii) Antecedent : The altitudes drawn on two sides of a triangle are congruent.
Consequent : Those two sides are congruent.

Here, BL and CM are the altitudes drawn on two sides AC and AB respectively of ∆ABC and are congruent, so side AB is congruent to side AC.