Question

Given: AB is the perpendicular bisector of IK.

Which statement can you conclude is true from the given information?

A. AJ=BJ
B. Angle IAJ is a right angle
C. IJ=JK
D. A is the midpoint of IK

Answer 1

its more than one answer
1)angle IAJ is a right angle
2)IJ=JK

Answer 2

The correct answer is C. IJ = JK

Explanation:

• Given: AB is the perpendicular bisector of IK.

⇒ AB divides the line segment IK in two equal parts i.e. IJ = JK and the angle formed at the point of intersection J is 90° ⇒ ∠AJI = 90°.

• In ΔAIJ, By angle sum property of a triangle

∠AJI + ∠AIJ + ∠IAJ = 180° ( But ∠AJI = 90° )

∠AIJ + ∠IAJ = 90° ⇒ ∠IAJ < 90°

So, ∠IAJ is not a right angle.

• Its not given IK is a perpendicular bisector so AJ = BJ need NOT be true.

• As A does not lie on the line IK so A can not be the mid point of IK.

Hence, we conclude the correct statement is IJ = JK