SOLUTION: write true or false after the statement. 1. All radii of two or more circles are congruent. 2. Radii of the same circle are congruent. 3. The endpoint of the radius lies in the

1. All radii of two or more circles are congruent.

Certainly not, because a huge monstrous radius of a huge monstrous
circle can't be congruent to a tiny little radius of a tiny little
circle.  

2. Radii of the same circle are congruent.

That's true.

 

OA and OB are congruent.

3. The endpoint of the radius lies in the interior of the circle.

 

One endpoint of radius AO is interior to the circle, because the center
O is interior to the circle, but the other endpoint A is not. It is on the
circle itself.  So I don't know how to answer this, unless your teacher
thinks the center of the circle is not to be called an endpoint of the
radius.

4. Diameters of the same circle are congruent.

 

Yes, AD and BC are congruent.


5. The endpoints of any chord of any circle lies on the circle.

 

Yes, both A and C lie on the circle.

6. A diameter is a chord.




Yes BC is a segment connecting two points on the circle.  So it's a chord. 

7. A chord is a diameter.

No, not necessarily at all. 

 

AC is a chord, but it certainly isn't a diameter!

8. Twice the length of the diameter is equal to the length of the radius.



Yes because BO and CO are both radii and congruent, so the length of 
diameter BC is twice the length of radius BO.

9. There exists a point x whose distance from the center of a circle is greater
than the radius, so point x lies on the interior of the circle.

No, for if you go further away from the center than the length of the radius 
of a circle, you go outside the circle.

10. There exists a point y whose distance from the center of a circle is less
than the radius, so point y lies on the interior of the circle.

Certainly there exist many such points. Look at this one:



Its distance from O is certainly less than the length of a radius.

Edwin