Question

1. choose the best answer. conjecture: intersecting lines form only vertical angles. diagram of lines ( ab ) and ( cd ) intersecting at ( e ), with points ( a, b, c, d ) labeled is this conjecture true?

• no, ( angle aed ) and ( angle bec ) are a counterexample.
• no, ( angle aeb ) and ( angle bec ) are a counterexample.
• yes.
• no, ( angle aeb ) and ( angle dec ) are a counterexample.

Explanation:

1. Recall the definition of vertical angles (opposite angles formed by intersecting lines) and adjacent angles (angles that share a common side and vertex).
2. Analyze each option:

• Option 1: $\angle AED$ and $\angle BEC$ are vertical angles, not a counterexample.
• Option 2: $\angle AEB$ and $\angle BEC$ share a common side ($EB$) and vertex ($E$), so they are adjacent angles (not vertical). This shows intersecting lines form non - vertical (adjacent) angles, so it's a counterexample to the conjecture that intersecting lines form only vertical angles.
• Option 3: The conjecture is false as intersecting lines form adjacent angles too.
• Option 4: $\angle AEB$ and $\angle DEC$ are vertical angles, not a counterexample.

Answer:

No, $\angle AEB$ and $\angle BEC$ are a counterexample.