Question

1. choose the best answer. conjecture: the noncommon rays of all adjacent angles form straight lines. three diagrams: first, points a, b, c in a line with ray bd; second, points e, f, g in a line with ray fh; third, point i, j with rays jl and jk is this conjecture true?

○ no, ∠ijk is a counterexample.
○ no, ∠abc is a counterexample.
○ no, ∠efg is a counterexample.
○ yes.

Explanation:

To determine if the conjecture is true, we analyze each angle:

• For \(\angle ABC\), the non - common rays \(BA\) and \(BC\) form a straight line (since \(A - B - C\) are colinear).
• For \(\angle EFG\), the non - common rays \(FE\) and \(FG\) form a straight line (since \(E - F - G\) are colinear).
• For \(\angle IJK\) (should be \(\angle IJL\) and \(\angle KJL\) as adjacent angles at \(J\)), the non - common rays \(JI\) and \(JK\) (or \(JI\) and \(JL\) and \(JK\) depending on adjacency) do not form a straight line. So \(\angle IJK\) (the adjacent angles at \(J\)) is a counterexample to the conjecture that the non - common rays of all adjacent angles form straight lines.

Answer:

No, \(\angle IJK\) is a counterexample.