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?
2 answers:
<span>AP¯¯¯¯¯≅DQ¯¯¯¯¯ is true</span>
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)]
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