Image A Image B The images above were constructed using Geometer\'s Sketchpad wh
ID: 3008636 • Letter: I
Question
Image A
Image B
The images above were constructed using Geometer's Sketchpad which is an interactive Dynamic Geometry mathematics visualization software.
Image A: Represents my final submission and pertains to my question(s) below.
I know that there has to be a relationship between mPR/ m RQ and m PX/mQX because when I moved points P, Q, and R independently of each other their measurements continue to remain the same dependent on point positions.
Here is my question(s): Is there a relationship between mPR / mRQ and mPX / mQX? And, what may the nature of this relationship be?
Please explain in detail.
Explanation / Answer
On using the given values , we find that
mPR/mRQ =10.32/10.52 = 0.98
and mPX/mQX=5.46/5.57 = 0.98
So clearly asboth ratios are equal, so
mPR/mRQ =mPX/mQX This is first answer.
And this result actually proves the angle bisector theorem of a triangle, that says that
" An angle bisector ( RX here) divides the opposite base in the same ratio ( here mPX/mQX) that is always equal the ratio of the included sides ( mPR/mRQ here) of that angle that is being bisected ( as here RX bisect angle PRQ)."
This is the nature of this given relation.
Answer