Given a segement with endpoints A and B, what figure can you construct using the steps below?

Question

Step 1: Draw a ray with endpoint C.

 

Step 2: Open the compass to the length of line AB.

 

Step 3: With the same compass setting, put the compass point on point C. Draw an arc that intersects the ray. Label the point of intersection D.

 

A) a perpendicular bisector

 

B) A congruent segment

 

C) an angle bisector

 

D) a congruent angle

 

( I don't have a compass right now so I can't really answer this question at the moment. Thank you for your help for whoever help!)

Answer 1

B)  A congruent segment

Answer 2

You don't actually need a compass to answer.  You really need to visualize what is happening.

 

By setting the compass to the length of AB, you are setting the radius of the circle it would create to be the same as the length of AB.

 

By creating the intersecting arc on the ray with C, you have just copied the length of AB to ray C.  This is why the AB and CD will be congruent.