Question

line t is the perpendicular bisector of fg. if line t intersects fg at point h, which of the following statements must be true? check all that apply. a. fg = fh b. line t intersects fg at a right angle c. line t is perpendicular to fg d. line t is parallel to fg e. point h is the midpoint of fg

Explanation:

Step1: Recall definition of perpendicular bisector

A perpendicular bisector of a line - segment is perpendicular to the line - segment and bisects it.

Step2: Analyze option A

Since \(H\) is the mid - point of \(\overline{FG}\), \(FG = 2FH\), not \(FG=FH\). So option A is false.

Step3: Analyze option B

By the definition of a perpendicular bisector, line \(t\) intersects \(\overline{FG}\) at a right angle. So option B is true.

Step4: Analyze option C

A perpendicular bisector is perpendicular to the line - segment it bisects. So line \(t\) is perpendicular to \(\overline{FG}\), and option C is true.

Step5: Analyze option D

A perpendicular bisector cannot be parallel to the line - segment it bisects. So option D is false.

Step6: Analyze option E

Since line \(t\) is the bisector of \(\overline{FG}\) and intersects \(\overline{FG}\) at \(H\), point \(H\) is the mid - point of \(\overline{FG}\). So option E is true.

Answer:

B. Line \(t\) intersects \(\overline{FG}\) at a right angle, C. Line \(t\) is perpendicular to \(\overline{FG}\), E. Point \(H\) is the midpoint of \(\overline{FG}\)