Question

question 5 of 5 select the correct answer. based on the construction shown which statement is true? ea = dc point e is the mid - point of line segment ab. the measure of angle abf is equal to the measure of angle cbf. the measure of angle abc is equal to the measure of angle cbf.

Explanation:

Step1: Analyze geometric construction

This appears to be an angle - bisecting construction. When constructing an angle bisector, arcs are drawn from the vertex of the angle (point B) with the same radius. The line drawn through the intersection of the arcs (line BF) divides the angle ∠ABC into two equal - measure angles.

Step2: Evaluate each option

• Option 1: There is no indication from the construction that \(EA = DC\).
• Option 2: There is no information in the construction to suggest that E is the mid - point of AB.
• Option 3: Since this is an angle - bisecting construction, by the definition of an angle bisector, the measure of angle \(\angle ABF\) is equal to the measure of angle \(\angle CBF\).
• Option 4: \(\angle ABC\) is the whole angle and \(\angle CBF\) is half of it, so they are not equal.

Answer:

The measure of angle \(\angle ABF\) is equal to the measure of angle \(\angle CBF\).