Question

p is the midpoint of segment QN, segment MP is perpendicular to segment QN. Prove triangle MRQ congruent to triangle MRN

Answer 1

Please Help me if Possible!

Answer 2

@Brg99 I'll help you. Let's work

Answer 3

Are you here?

Answer 4

Yes

Answer 5

@ash2326 Sorry about that, I'm ready to begin.

Answer 6

Anyone that could please help?

Answer 7

In triangles RPQ and RPN
QP=PN since MP bisects QN
RP=RP
angle RPQ=angle RPN=90 degrees
do you get this?

Answer 8

Yes

Answer 9

so by SAS congruency triangles RPQ and RPN are congruent.

Answer 10

By CPCT , angle QRP = angle NRP
and QR=NR
do you get this?

Answer 11

That makes sense.

Answer 12

We already have
angle QRP=angle NRP
so
180-angle QRP=180-angle NRP
Can you tell what these angles are?

Answer 13

Linear Pairs

Answer 14

180-angle QRP= angle QRM
do you get this?

Answer 15

Yes

Answer 16

so what's 180-angle NRP?

Answer 17

Angle NRM

Answer 18

How would I write this in a two column proof?

Answer 19

Good :)
180-angle QRP=MRQ ( supplementary angles)
180-angle NRP=MRN ( supplementary angles)
therfore angle MRQ=angle MRN

Answer 20

For column proof we need to have properties cited at every step

Answer 21

Yes

Answer 22

Can you prove the two triangles congruent ?

Answer 23

Well we We have that <MRQ = <MRN, and QR = NR we would need one more angle or side to prove the triangles congruent.

Answer 24

what about MR?

Answer 25

Oh right due to the reflexive property MR = MR, so we have SAS. Now could you help me put this in a Two column proof?

Answer 26

OK, I will be back in 20 minutes or so, till then you try to put this

Answer 27

Sure

Answer 28

I am sort of crunched for time, but I should be here in 20 minutes, Thanks for your help.

Answer 29

Welcome. BRB:)

Answer 30

Hello?

Answer 31

Hi, I'm back. Did you try?

Answer 32

Yes