Question

BC and DE are chords of circle A, and BC DE. Which statement cannot be verifiedfrom the information that is given?BC DEBZBACZ ZDAEAABC = AADEZDAE CAD

Answer 1

Let's start in the first information:

`arcBC\cong arcDE`

This can be verified, because, AC, AB, AD and AE are all congruent, because they are the radius of A and, since BC and DE are congruent, triangles ABC and ADE are also congruent.

Thus, the angles mBAC and mDAE are congruent. The measure of thesee angles are the same as the arcs BC and DE, so we verified this alternative.

In the explanation above, we also verified the second alternative:

`\angle BAC\cong\angle DAE`

And we verified the third alternative:

`\Delta ABC\cong\Delta ADE`

We are left with the last alternative:

`\angle DAE\cong\angle CAD`

This can't be verified. One way of seeing that is that we can rotate triangle ABC around the circle without changing any of the given information, however this changes mCAD.

So the only statement that cannot be verified from the given information is the last one:

`\angle DAE\cong\angle CAD`