(a) In triangles ABC and DEF, it is given that ∠A=∠D and AB=DE=BC=EF.
(i) A student claims that "there is insufficient information to determine whether triangles ABC and DEF are congruent". Do you agree? Explain your answer.
(ii) In triangle OPQ with in-centre I (ie. ∠OPI=∠QPI) and circumcentre J (ie. OJ=PJ=QJ), it is given that P, I and J lies on a straight line. Show that OP=QP.
(b) In triangles ABC and DEF, it is given that ∠A=∠D≥90[suptag]o[/suptag], AB=DE and BC=EF.
(i) Show that sin∠C=sin∠F
(ii) A student claims that "there is insufficient information to determine whether triangles ABC and DEF are congruent". Do you agree? Explain your answer.
(c) In triangles ABC and DEF, it is given that ∠A=∠D and AB=DE≤BC=EF.
(i) Show that ∠C≤∠A<180[suptag]o[/suptag]-∠C.
(ii) A student claims that "there is insufficient information to determine whether triangles ABC and DEF are congruent". Do you agree? Explain your answer.
