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do you agree that if two lines intersect at the center of a circle ,then the lines intercept two pairs of congruent arcs? explain your answer.


Sagot :

Yes.  Vertical Angle Theorem in a circle:  If two line intersects at the center of the circle, they form two pairs of congruent non-adjacent central angles.

The measure of central angle is equal to the arc it intercepts.

Therefore, the arcs intercepted by the two pairs non-adjacent central angles formed by two lines intersecting at the center are congruent.