Construct an Argument In the figure at the right, AE = DB and C is the midpoint of \(\overline{\text{AE}}\) and \(\overline{\text{DB}}\). Complete the proof to show that AC = CB.

Given: AE = DB and C is the midpoint of \(\overline{\text{AE}}\) and \(\overline{\text{DB}}\)

Prove: AC = CB

Proof: Since C is the midpoint of _____ and _____, AC = CE = \(\cfrac{1}{2}\) _____ and DC = CB = \(\cfrac{1}{2}\) _____ by the definition of midpoint. We are given AE = DB. By the _____ Property of Equality, \(\cfrac{1}{2}\)AE = \(\cfrac{1}{2}\)DB. So, by _____, AC = CB.

Construct an Argument Refer to the figure at the right. Complete the two-column proof to show if m∠3 = 2x - 15 and m∠6 = x + 55, then x = 70.

Given: j || k, transversal l; m∠3 = 2x - 15, m∠6 = x + 55

Prove: x = 70

Construct an Argument Refer to the figure at the right. Complete the two-column proof to show if ∠ABE and ∠DBC are right angles, then m∠ABD = m∠EBC.

Given: ∠ABE and ∠DBC are right angles

Prove: m∠ABD = m∠EBC