Question

Construct an isosceles triangle, given its base and base angle and justify the construction.

Answer 1

Steps:

• Draw a line segment AB of any given length. 
• Construct ∠BAX and ∠ABY at A and B such that ∠A = ∠B
• \(\overrightarrow {AX}\) and \(\overrightarrow {BY}\) will intersect at C. 
• ΔABC is the required triangle.

Justification: 

Drop a perpendicular CM to AB from C. 

Now in ΔAMC and ΔBMC 

∠AMC = ∠BMC [Right angle] 

∠A = ∠B [Construction] 

CM = CM (Common) 

∴ ΔAMC ≅ ΔBMC 

⇒ AC = BC [CPCT]