Problema Solution
Write a proof with the give and prove:
Given: LP is perpendicular to EA, N is the midpoint of ray LP, P and R trisect ray EA.
Prove: Triangle PEN is similar to triangle PAL
Answer provided by our tutors
Proof :
Let the length of the side LP be a and the length od side EA be b . then the EP = b/3 and PA = 2b/3.
LN = a/2 and NP = a/2.
So,we can have
NP/LP = (a/2)/a = 1/2
EP/PA = (b/3)/(2b/3) = 1/2
This means that
NP/LP = EP/PA ------(1)
Now the Line LP is perpendicular to EA this means ,
angle EPN = angle APL = 90 degrees ----(2)
Now we have:
Two sides have lengths in the same ratio, and the angles included between these sides have the same measure
So we can say that PEN is similar to triangle PAL.