Question

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?

Answer 1

AP¯¯¯¯¯≅DQ¯¯¯¯¯ is true

Answer 2

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)]