Question

A student used a compass and a straightedge to construct
`\overline{CE}` in ABC. Which statement must always be true for this construction?(1) ∠CEA, ∠CEB(2) ∠ACE, ∠BCE(3)
`\overline{AE}, \overline{BE}`(4)
`\overline{EC}, \overline{AC}`

Answer 1

2) ∠ACE ≅ ∠BCE

Explanation:

Considering the complete question attached in Figure below, geometry shows that ∠ACB is bisected into two angles ∠ACE and ∠BCE and we know that bisection means to divide an angle into two equal angles. According to this the resultant angles ∠ACE and ∠BCE must be equal and congruent.