Question

jamika started with ray cd and line segment ab and constructed ce. which statement, if true, guarantees that $overline{ce}$ is congruent to $overline{ab}$? choose 1 answer: a $overline{ab}congoverline{cd}$ b $ce = 2ed$ c circle c is congruent to circle a. d circle c intersects circle a.

Explanation:

Step1: Recall congruent - segment construction

In geometric construction of congruent segments, if we want to construct a segment $\overline{CE}$ congruent to $\overline{AB}$, we use circles with equal radii. When circle $C$ is congruent to circle $A$, and we use the radius - length property of circles. If we set the radius of circle $A$ equal to the length of $\overline{AB}$ and the radius of circle $C$ equal to the length of $\overline{CE}$, when the circles are congruent, the radii are equal. So, if circle $C$ is congruent to circle $A$, then $\overline{CE}\cong\overline{AB}$.

Step2: Analyze other options

Option A: $\overline{AB}\cong\overline{CD}$ does not directly relate $\overline{CE}$ and $\overline{AB}$. Option B: $CE = 2ED$ gives a relationship within segment $\overline{CD}$ and not between $\overline{CE}$ and $\overline{AB}$. Option D: Just because circle $C$ intersects circle $A$ does not guarantee that $\overline{CE}\cong\overline{AB}$.

Answer:

C. Circle $C$ is congruent to circle $A$.