Question

PLEASE HELP ASAP 45 POINTS !!!!

Answer 1

Answer:

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

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

Step-by-step explanation:

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)

$\frac{1}{2} AB$  ≅  $\frac{1}{2} CD$

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

Answer:

Option 4 and option 2

Step-by-step explanation:

Given: The line segment AB & CD, P is the midpoint of AB ⇒ AP=PB and Q is the midpoint of CD ⇒ CQ=QD.

Also, It is given that P is point on AB, therefore there is no relation of point P with line segment CQ.

Hence, the invalid statement is

Segment AP is congruent to segment PQ.

Hence, option (D) is correct.

Now, it is given that R is the midpoint of AP ⇒ AR=RP and S is the midpoint of QD ⇒ QS=SD

AB≅CD (Given)

$\frac{1}{2}AB$≅$\frac{1}{2}CD$

PB≅CQ (Mid points are given)

Therefore, PA=QD

⇒PR=QS

Also, because PB≅CQ⇒PB+PR≅CQ+QS

⇒RB≅CS

⇒Segment RB is congruent to segment CS

Hence, option 2 is correct.