1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
HACTEHA [7]
2 years ago
5

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines

l and m are parallel. Angles 1 and 2 are supplementary by definition. Upload the entire proof below.
Given:
∠1 and ∠2 are supplementary angles
Prove:
l || m



STATEMENT REASON
1.∠1 and ∠2 are supplementary angles 1. Given
2. m∠1 + m∠2 = 180° 2.
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. 4.
5. m∠1 + m∠2 = m∠1 + m∠3 5.
6. 6.
7. l || m 7.
Mathematics
1 answer:
lisabon 2012 [21]2 years ago
6 0

To enable the completion of the proof that line <em>l</em> is parallel to line <em>m</em>, a

diagram showing the lines and their common transversal is attached.

The completed two column proof is presented as follows;

Statement  {}                                                      Reason

1. ∠1 and ∠2 are supplementary angles  {}   1. Given

2. m∠1 + m∠2 = 180°   {}                                 2. <u>Definition of supplementary ∠s</u>

3. ∠1 and ∠3 are supplementary angles  {}  3. Exterior sides in opposite rays  

4. <u>m∠1 + m∠3 = 180° </u>    {}                                4. <u>Definition of supplementary ∠s</u>

5. m∠1 + m∠2 = m∠1 + m∠3      {}                   5. <u>Transitive property of equality</u>

6. <u>m∠2 = m∠3 </u>     {}                                        6. <u>Subtraction property of equality</u>    

7. l ║ m      {}                                                   7. <u>Converse of alternate interior </u>

    {}                                                                      <u>angles postulate</u>

Reasons:

  • Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°

  • Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)

  • Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles

  • Reason for statement 5: Transitive property of equality describes the property that if a number <em>x</em> = <em>y</em>, and <em>z </em>= <em>y</em>, then <em>x</em> = <em>z</em>.

  • Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality

  • Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two  lines and a common transversal are congruent, the two lines are parallel.

Learn more here:

brainly.com/question/25178453

You might be interested in
Answer the following questions please.<br><br> Urgent.
djverab [1.8K]

Answer: What is the questions

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Identify the domain of the graph given. *Don't forget the parenthesis or brackets*​
anzhelika [568]

Answer:

(-4,3)

Step-by-step explanation:

The domain of a function is all of its possible x-values.  In this graph, there is a y-value for every x-value between -4 and 3 except -4 and 3, because there are open dots at those points.  Therefore, the domain is (-4,3).  Use parenthesis because the function is not defined at x=-4 or x=3.

5 0
3 years ago
If the radius of a circle is 6 centimeters, what is its area?
Serggg [28]

Answer:

113

Step-by-step explanation:

p x r^2 =

pie x 6^2 = 113.097…

5 0
3 years ago
Read 2 more answers
2+2×4 that is my question i need help​
devlian [24]

Answer:

10

Step-by-step explanation:

2+(2x4)

2x4=8

2+8=10

6 0
2 years ago
Read 2 more answers
117,456 rounded to nearest tenth
tatuchka [14]
117,460 is the answer
4 0
3 years ago
Read 2 more answers
Other questions:
  • Jennifer is a car saleswoman. She is paid a salary of $2000 per month plus $500 for each car that she sells. Her salary can be m
    12·1 answer
  • Which numbers produce An irrational number when added to 0.4
    5·2 answers
  • Which of the following is equivalent to the expression (3ab)(-5ab)?
    14·1 answer
  • In which quadrant of the coordinate graph does point J lie?
    6·1 answer
  • Ty sold 50 tickets this is 40% of how many he has to sell how many tickets must he sell
    8·1 answer
  • At the local pet store, zebra fish cost $1.85 each and neon tetras cost $2.10 each. If Yumi bought 11 fish for a total cost of $
    12·2 answers
  • briana records the race times for a track meet. she records for 5 groups of 4 student's each . how many observations does she ma
    9·1 answer
  • A bag fertilizer weighs 6 1/2 ib. How much does 1 1/3 Bags of fertilizer weighs
    12·1 answer
  • Let angle 1, angle 2, and angle 3 have the following relationships.
    13·1 answer
  • If two pyramids are similar and the ratio between the lengths of their edges is
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!