Ab is congruent to cd. point p is the midpoint of ab, and point q is the midpoint of cd. which relationship must be true?

Solution:

AB ≅ CD[Given]

⇒Point P is the midpoint of AB, and point Q is the midpoint of CD.

→AP≅BP[Given]

AP=BP(1)

→C Q ≅ Q D[Given]

C Q=Q D(2)

⇒AB=CD

→AP+BP=CQ+QD

→AP+AP=CQ+CQ[Using (1) and (2)]

→2 AP=2 C Q

→AP=CQ

→BP=QD

⇒AP=BP=CQ=QD[Using (1) and (2)]

irrational, cannot