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 these two sides are congruent.

Answer 1

i. Two equilateral triangles are similar. 

Conditional statement: “If two triangles are equilateral, then they are similar. 

Antecedent (Given): Two triangles are equailateral. 

i.e. ∆ABC and ∆PQR are equilatral triangle. 

Consequent (To prove): Triangles are similar i.e. ∆ABC ∼ ∆PQR

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

Antecedent (Given): Angles in a linear pair are congrunent. 

∠ABC and ∠ABD are angles in a linear pair 

i.e. ∠ABC = ∠ABD 

Consequent (To prove): Each angle is a right angle. 

i.e. ∠ABC – ∠ABD = 90°

iii. If the altitudes drawn on two sides of a triangle are congruent, then these two sides are congruent. 

Antecedent (Given): Altitude drawn on two sides of triangle are congrunent. 

In ∆ABC, AD ⊥ BC . and BE ⊥ AC. seg AD ≅ seg BE 

Consequent (To prove): Two sides are congruent. 

side BC ≅ side AC A