Hi! given that u || v and m< 3= m< 1, prove that v || w

Question

While I can’t add a photo, 1 & 2 are corresponding sitting on lines u & v, 3 is alt exterior angles with 1 (sitting on line w)

Might not be able to answer without photo, however :(

Answer 1

OK here's how I drew it...

line v underneath u, and w underneath v...

so from north to south is u,v,w

stray line slices them

Let angle x be the vertical angle across from 1...

Let angle y be the vertical angle across from 2...

Let angle z be the vertical angle across from 3...

with respect to line u:

so on the "northeast corner of the junction is 1 and

then "southeast corner of the junction is x

with respect to line v:

so on the "northeast corner of the junction is 2 and

then "southeast corner of the junction is y

with respect to line w:

so on the "northeast corner of the junction is z and

then "southeast corner of the junction is 3

the proof follows from this chain of angle equalities,

which goes like this:

angle z = angle3 (vertical)

= angle1 (given)

= angle x (vertical)

= angle y ( corresponding via parallel u and v)

= angle 2 (vertical)

since all of these angles are equal, the three lines

must be parallel by converse theorem (lines cut by stray

such that corresponding angles are congruent forces parallel)