geometric proof

[troy_jeremy]

i have a diamond-shaped figure with a line segment PN appearing to be through the center. the two other points on the diamond are M and S. On line PN is point Q. Line MQ and line SQ are diagnol.

I am given that MN=MS and MP=PS.

how do i prove that angle MQP=angle SQP?

please and thank you!

 

[pka]

I cannot understand the problem above just from your description.
Do you know how to use a graphics program such as PAINT.
You could draw the diagram. Save it as *.gif format.
Upload it to a image site such as http://www.imageshack.us/.
Then display it in your message.

 

[troy_jeremy]

 

[jacket81]

problem

I think might have a typo.
Don't you mean MN = NS, instead of MN = MS?

 

[troy_jeremy]

yes, that is a typo.

*MN=NS*

sorry

 

[jacket81]

problem

Okay, since mn = ns, mp =ps, and pn= pn, then by SSS, triangles pmn and psn are congruent.
So, since those triangles are congruent, then angle mpq = spq.
So, since mp = sp, pq = pq, and angle mpq = spq, then by SAS, triangles mpq and spq are congruent.
Since those triangles are congruent, then angle mqp = sqp!

 

[troy_jeremy]

thanks!