Question

proving parallel lines with alternate exterior angles. given: <1 = <2 prove: p || q
assemble the proof by dragging tiles to the statements and reasons columns.
angles: ~= , <1 , <2 , <3,
lines: | | , p , q ,
statements: <1 and <3 are vertical reasons: given , transitive property , vertical angles theorem , def. of vertical

Answer 1

Answer:

Statements                                 Reasons

1. <1 ≅ <2                                     1.  given

2. <1 and <3 are vertical <s        2.  def. of vertical <s

3. <1 ≅ <3                                    3.  vertical angles theorem

4. <2 ≅ <3                                   4.  transitive property

5.  p ll q                                       5.  converse of corresponding angles theorem

Step-by-step explanation:

Got it 100% on edge 11/24/2020

Answer 2

Parallel lines are lines that do not intersect.

The complete proof and reason is:

1. $\mathbf{ \angle\ 1\ \cong\ \angle\ 2}$   ----- Given
2. $\mathbf{ \angle\ 1\ and \ \angle\ 3\ are\ vertical}$ ------ Definition. of vertical angles
3. $\mathbf{ \angle\ 1\ \cong\ \angle\ 3}$  ------ vertical angle theorem
4. $\mathbf{ \angle\ 2\ \cong\ \angle\ 3}$  ---- transitive property
5. $\mathbf{a\ ||\ b}$ ------ converse of corresponding angles theorem

From the question, we are given that:

$\mathbf{ \angle\ 1\ \cong\ \angle\ 2}$ ----- this represents the first statement

So, the second statement is:

$\mathbf{ \angle\ 1\ and \ \angle\ 3\ are\ vertical}$

Because they are vertical angles, then they are congruent.

So, we have:

$\mathbf{ \angle\ 1\ \cong\ \angle\ 3}$

Transitive property states that:

$\mathbf{ if \ a = b\ and\ b = c, \ then\ a = c}$

In (1), and (2), we have:

$\mathbf{ \angle\ 1\ \cong\ \angle\ 2}$ and $\mathbf{ \angle\ 1\ \cong\ \angle\ 3}$

This means that:

$\mathbf{ \angle\ 2\ \cong\ \angle\ 3}$

At this point, we have proved that both lines are parallel.

i.e.

$\mathbf{a\ ||\ b}$

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