Question 69
Point $D$ lies on side $BC$ of triangle $ABC$. Angle $A$ in triangle $ABD$ is equal to angle $C$ in triangle $ABC$, and angle $A$ in triangle $ACD$ is equal to angle $B$ in triangle $ABC$.
The given information is not enough to derive the exact shape of triangle $ABC$. However, you can still derive that one of the given statements below is *always* false. Which statement is it?
By $|AB|$ we denote the length of line segment $AB$.
A) $|AD| \lt |AC|$
B) $|AC| \lt |AB|$
C) $|AB| \lt |BC|$
D) $|AD| \times |CD| \lt |AB| \times |AC|$
E) $|AB| \times |AC| \lt |AD| \times |BC|$
The given information is not enough to derive the exact shape of triangle $ABC$. However, you can still derive that one of the given statements below is *always* false. Which statement is it?
By $|AB|$ we denote the length of line segment $AB$.
A) $|AD| \lt |AC|$
B) $|AC| \lt |AB|$
C) $|AB| \lt |BC|$
D) $|AD| \times |CD| \lt |AB| \times |AC|$
E) $|AB| \times |AC| \lt |AD| \times |BC|$