Answer:
The two pieces of information are needed to prove that line AB is a perpendicular bisector of line CD are:
m∠AGD = 90° ⇒ B
CG = GD ⇒ C
Step-by-step explanation:
If line m is the perpendicular bisector of line AB and intersect it at point D
- The angles around point D are right angles (the measure of each one 90°)
Let us use these facts to solve our question
Look at the given figure
∵ Line AB is the perpendicular bisector of line CD
∵ Line AB intersects line CD at point G
∴ G is the midpoint of CD
→ That means the point G divides the line CD into two equal parts
CG and GD
∴ CG = GD
∵ AB ⊥ CD at G
∴ ∠AGD and ∠AGC are right angles
→ the measure of the right angle is 90°
∴ m∠AGD = m∠AGC = 90°
The two pieces of information are needed to prove that line AB is a perpendicular bisector of line CD are:
m∠AGD = 90° ⇒ B
CG = GD ⇒ C
