Answer:
See answers below
Explanation:
44.)
premises: VA is parallel (P) to LI, <1 = <2 , and <3 = <4
Since the segments VA and LI are parallel, then angles <1 and <3 are equal because they are "corresponding angles" among parallel lines.
That means: <1 = <3 which at a time is equal to <4, and since <1 = <2, then for transitive property <2 must equal <4. And this is the condition for parallel lines (or segments). therefore LA P DI
45.)
Premises: <G = <E and <G = <M
Then for transitive property, <E = <M, which both share the same segment of line, and therefore verify the property of internal alternate angles among parallel lines.
46.)
Premises: MQ P NP, <4 = <3 , and <1 = <5
Since <2, <3 and <4 add to 180 degrees, then <2 = 180 - <3 - <4
and since <3 = <4 when can write that expression as:
<2 = 180 - <3 - <3
On the other hand, since <3 and <5 must be equal because they are internal alternate angles among parallel segments, one can replace <3 by <5 in the previous expression, resulting in:
<2 = 180 - <5 - <5 which we can also write as: <5 = 180 - <5 - <2
Now, since in the triangle MNQ angles <1, <2 and <5 should add up to 180 degrees, we can write that <1 = 180 - <5 - <2
Notice that the right hand side of the last two expression comparing angles are exactly the same: 180 -<5 -<2
therefore, using transitive property, <5 must equal <1