Question

Select the correct answer from each drop-down menu.

AB - CD Point Pis the midpoint of AB. Point Q is the midpoint of CD. Point Ris the midpoint of AP. Point Sis the midpoint of QD
is an invalid relation.
Because point Ris the midpoint of AP and point Sis the midpoint of QD
we can conclude that

Answer 1

The invalid statement is 4) Segment AP is congruent to segment PQ.

We conclude that 2) Segment RB is congruent to segment CS.

Explanation:

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Given, line segment AB & CD

Here, P is the midpoint of AB ⇒ AP=PB

& Q is the midpoint of CD ⇒ CQ=QD

It is given that P is point on AB not on CD ∴ there is no relation of point P with line segment CQ.

Hence, the invalid statement is

Segment AP is congruent to segment PQ.

Now, given that R is the midpoint of AP ⇒ AR=RP

& S is the midpoint of QD ⇒ QS=SD

AB≅CD (Given)

≅

PB ≅ CQ (∵from midpoint statements)

∵ PA=QD ⇒ PR=QS

Because PB≅CQ

PB+PR≅CQ+QS

⇒ RB≅CS

Therefore, Segment RB is congruent to segment CS

Answer 2

Segment AP is congruent to segment PQ

Segment RB is congruent to segment CS

Explanation: