Circle S and Circle U are congruent circles.
The figure shows two circles with their center labeled as Upper S and Upper U. The two circles overlap each other such that they intersect at points Upper R and Upper T. Dotted lines are drawn from the point Upper S to Upper T, Upper T to Upper U, Upper U to Upper R, Upper U to Upper R, and Upper S to Upper U.
Name three radii of Circle S.
Name three radii of Circle U.
How are the radii of the two circles related? Explain your reasoning.
what does it mean to be congruent?
I can help you
To name three radii of Circle S, we need to identify three line segments that connect the center of Circle S (labeled as Upper S) to three different points on the circle. In this case, we can choose any three points where Circle S is intersected by the dotted lines. Let's name these points as Upper P, Upper Q, and Upper M. So, the radii of Circle S would be Upper SP, Upper SQ, and Upper SM.
Similarly, to name three radii of Circle U, we need to identify three line segments that connect the center of Circle U (labeled as Upper U) to three different points on the circle. In this case, we can choose any three points where Circle U is intersected by the dotted lines. Let's name these points as Upper V, Upper W, and Upper X. So, the radii of Circle U would be Upper UV, Upper UW, and Upper UX.
The radii of the two circles (Circle S and Circle U) are related because they are congruent. Congruent circles have the same size and shape, which means their radii are equal in length. In this case, Upper SP is equal in length to Upper UP, Upper SQ is equal in length to Upper UQ, and Upper SM is equal in length to Upper UM. Similarly, Upper UV is equal in length to Upper SV, Upper UW is equal in length to Upper SW, and Upper UX is equal in length to Upper SX. This equivalence of radii is due to the circles being congruent.