Question

if c is the mid - point of $overline{ab}$ and $overline{de}$, what is the length of $overline{ab}$? (1 point)

Explanation:

Step1: Prove triangles congruent

Since C is the mid - point of AB and DE, we have AC = BC and DC = CE. Also, ∠ACD = ∠BCE (vertically opposite angles). By the Side - Angle - Side (SAS) congruence criterion, △ACD≅△BCE.

Step2: Find length of AC

In right - triangle ACD, using the Pythagorean theorem \(AC=\sqrt{AD^{2}+DC^{2}}\). Given AD = 5 and DC = 12, then \(AC=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\).

Step3: Calculate length of AB

Since C is the mid - point of AB, AB = 2AC. Substituting the value of AC = 13, we get AB = 2×13 = 26.

Answer:

26