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PLEASE HELP ASAP 45 POINTS !!!!
select the correct answer from each drop-down menu . AB ~= CD. point P is the midpoint of AB. Point Q is the midpoint of CD. Point R is the midpoint of AP . a
Point S is the midpoint of QD. ________ is an invalid relation.
because point R is the midpoint of AP and point S is the midpoint of QD , we can conclude that ________
•options for first blank 1.) segment QD is congruent to segment AP 2.) segment PB is congruent to segment CQ 3.) segment QD is congruent to segment PB 4.) Segment AP is congruent to segment PQ 5.) segment CQ is congruent to segment AP
•options for second blank 1.) segment RP is congruent to segment CS 2.) segment RB is congruent to segment CS 3.)segment RB is congruent to segment SD 4.) segment AR is congruent to segment CS 5.) segment RB is congruent to segment QS

Respuesta :

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)

[tex]\frac{1}{2} AB[/tex]  ≅  [tex]\frac{1}{2} CD[/tex]

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



jayilych4real

The invalid statement is

  • Segment AP is congruent to segment PQ.

Our conclusion is that:        

  • Segment RB is congruent to segment CS.

What is a Congruent Segment?

This refers to the segments which are equal in length and can be found by using the midpoints of each segment.

Hence, we can see that based on the line segment AB & CD,

  • P is the midpoint of AB ⇒ AP=PB
  • Q is the midpoint of CD ⇒ CQ=QD

Because P is point on AB not on CD, therefore there is no relation of point P with line segment CQ.

Therefore, the invalid statement is

  • Segment AP is congruent to segment PQ.

Now, to prove congruency,

  • PB ≅ CQ    (from midpoint statements)
  • PA=QD ⇒ PR=QS

Based on the fact that PB≅CQ  

PB+PR≅CQ+QS

⇒ RB≅CS

Therefore, Segment RB is congruent to segment CS

Read more about congruent segment here:
https://brainly.com/question/82457

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