Regarding a triangle $ABC$ and a point D taken on the side $AB$ of this triangle, it is known that two of the following four statements are true and two are false. I. $\mathrm{AB} \perp \mathrm{CD}$ II. $|\mathrm{AD}| = |\mathrm{BD}|$ III. $m(\widehat{ACD}) = m(\widehat{BCD})$ IV. $A(\stackrel{\triangle}{\mathrm{ACD}}) = A(\stackrel{\triangle}{\mathrm{BCD}})$ Accordingly, which of the following are the true statements for this triangle? A) I and II B) I and III C) I and IV D) II and III E) II and IV
Regarding a triangle $ABC$ and a point D taken on the side $AB$ of this triangle, it is known that two of the following four statements are true and two are false.
I. $\mathrm{AB} \perp \mathrm{CD}$
II. $|\mathrm{AD}| = |\mathrm{BD}|$
III. $m(\widehat{ACD}) = m(\widehat{BCD})$
IV. $A(\stackrel{\triangle}{\mathrm{ACD}}) = A(\stackrel{\triangle}{\mathrm{BCD}})$
Accordingly, which of the following are the true statements for this triangle?
A) I and II
B) I and III
C) I and IV
D) II and III
E) II and IV