Question

Please help (geometry)

Answer 1

Answer:

The statement BI = BK is true from the given information ⇒ B

Step-by-step explanation:

If a line is a perpendicular bisector of a line segment, then

• The line intersects the line segment in 4 right angles

• The line intersects the line segment in the mid-point of the line segment

• Any point on the line is equidistant from the endpoints of the line segment

Let us find the true statement

∵ Line AB is the perpendicular bisector of segment IK

→ By using the 1st note above

∴ AB ⊥ IK

∴ ∠IJA, ∠KJA, ∠IJB, ∠KJB are right angles

→ By using the 2nd note above

∴ J is the mid-point of IK

∴ IJ = JK

∵ Any point on line AB is equidistant from The endpoints of IK ⇒ 3rd note

∴ AI = AK

∴ BI = BK

∴ The statement BI = BK is true from the given information