Given: Lines a and b are parallel and line c is a transversal. Prove: Angle2 is supplementary to Angle8 Horizontal and parallel lines a and b are cut by transversal c. On line a where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line b where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is the missing reason in the proof? Statement Reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

Answer:

The correct option is;

Corresponding angles theorem

Step-by-step explanation:

Type of lines of lines a and b = Horizontal and parallel lines

The transversal to a and b = Line c

The angles between a and c labelled clockwise from the upper left quarter segment =  1, 2, 4 and 3

The angles between b and c labelled clockwise from the upper left segment =  5, 6, 8 and 7

Therefore, we have;

Statement   [tex]{}[/tex]                                                   Reason

1. a║b, c is a transversal   [tex]{}[/tex]                             Given

2. ∠6 ≅ ∠2       [tex]{}[/tex]                                              Corresponding angles theorem

3. m∠6 = m∠2       [tex]{}[/tex]                                         Definition of congruent

4. ∠6 is supp. to ∠8        [tex]{}[/tex]                               Definition of linear pair

5. ∠2 is supp. to ∠8        [tex]{}[/tex]                               Congruent supplement theorem

Corresponding angles are the angles located in spatially similar or matching corners of two lines that have been crossed by the same transversal. When the two lines having a common transversal are parallel, the corresponding angles will be congruent.                        

Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you deposit this amount at the beginning of each month in an account that credits 0.75% interest monthly, how long will it take you to attain your goal?

A cylinder has a height of 5.3cm and a diameter of 3.0cm. What is its volume

In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season.

Variable DF Estimate SE T
Intercept 1 −5.0 0.26 −19.3
WHIP 1 6.8 0.14 47.4
Which of the following statements is the best interpretation of the value 6.8 shown in the output?

a. ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP.


b. WHIP is predicted to increase by 6.8 units for each 1 unit increase of ERA.


c. For a pitcher with 0 units of WHIP, the ERA is predicted to be approximately 6.8 units.


d. For a pitcher with 0 units of ERA, the WHIP is predicted to be approximately 6.8 units.


e. Approximately 6.8% of the variability in ERA is due to its linear relationship with WHIP.

29points!
Match the vocab word with the definition:
.1Devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed
2.

An expression that consists of numbers, operations, and sometimes grouping symbol.
3.

The order in which operations must be computed when more than one operation is involve.
4.

A number representing how many times the base number should be multiplied by itself.
5.

A Symbol that represents a value that can change.
6.

A single number or variable, or numbers and variables multiplied together.
7.

The numerical factor in a term. A number being multiplied by a variable.
8.

A number on its own, it has a fixed value.
9.

A combination of variables, numbers, and operations.
10.

You replace, or substitute, all the variables with numbers and then simplify.
11.

A statement that the values of two math expressions are equal (indicated by the sign =).
12.

The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
13.

The symbol of a math operation.

plus, minus, times, divided by, equals
14.

An equation or inequality containing one or more variable
Open Sentence

Exponent (Power)

Numerical Expression

Operator

Term

Evaluate

Order of Operations

Grouping Symbol

Constant

Coefficient

Variable Expression

Equation

Inequality

Variable

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