Given: g ∥ h and ∠2 ≅ ∠3
prove: e ∥ f

statements reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorme
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
what is the missing reason in the proof?

a. vertical angles theorem
b. alternate exterior angles theorem
c. converse corresponding angles theorem
d. converse alternate interior angles theorem

 Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Given: g ∥ h and ∠2 ≅ ∠3

    Statements                               Reasons

1.g || h                               1. given

2.∠1 ≅ ∠2                               2.corresponding angles theorem

3.∠2 ≅ ∠3                               3. given

4.∠1 ≅ ∠3                                4. transitive property

5.e || f                                      5. Converse alternate interior angles.

As we know that if alternate angles are equal then two lines would be parallel using converse alternate interior angles.

Hence, Option 'D' is correct.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: