In the given figure, AB=AC and ∠GBC=∠HCB=90∘.
Which of the following statements is true?
(i) ΔBAC is isosceles ….. (given)
(ii) ∠ABC=∠ACB=x∘ (say) (base angles of an isosceles triangle)
(iii) ∠GBC=∠HCB=90∘ .. (given)
(iv) ∴∠GBA=∠HCA=90−x∘
In ΔGBA and ΔHCA
(v) ∠GBA=∠HCA (from (iv))
(vi) AB=AC …(given)
(vii) ∠GAB=∠HAC .….(vertically opposite angles are equal)
(viii) ΔGBA≅ΔHCA …… (ASA postulate)
⇒BG=CH and AG=AH ...(CPCT)