Question

The lines k and m are parallel and cut by a transversal line t.



A diagram.Short description, A diagram.,Long description,
On line k where it intersects line t, 4 angles are created. Labeled clockwise, from left: blank, angle 1, blank, angle 2.
On line m where it intersects line t, 4 angles are created. Labeled clockwise, from left: blank, angle 3, blank, angle 4.

Question
Move the angles and phrases into the blanks to complete the proof that angle 2 is congruent to angle 3.

Response area with 9 blank spaces
Statement

Reason

line k is parallel to line m

Given

Blank space 28 empty
is congruent to
Blank space 29 empty

Blank space 30 empty

Blank space 31 empty
is congruent to
Blank space 32 empty

Blank space 33 empty

Blank space 34 empty
is congruent to
Blank space 35 empty

Blank space 36 empty


Answer options with 7 options.

Answer 1

To complete the proof that angle 2 is congruent to angle 3, we can use the properties of parallel lines cut by a transversal. Here’s how you can fill in the blanks:

**Statement**:

1. **Line k is parallel to line m.**
**Reason:** Given

2. **Angle 1 is congruent to Angle 3.**
**Reason:** Alternate interior angles (since k || m and t is a transversal)

3. **Angle 2 is supplement to Angle 1.**
**Reason:** Linear pair (angles adjacent to each other on the same line)

4. **Angle 3 is supplement to Angle 4.**
**Reason:** Linear pair (angles adjacent to each other on the same line)

5. **Angle 1 + Angle 2 = 180°**
**Reason:** Definition of supplementary angles

6. **Angle 3 + Angle 4 = 180°**
**Reason:** Definition of supplementary angles

7. **Since angle 3 is congruent to angle 1, then angle 2 is also congruent to angle 3.**
**Reason:** Transitive property of equality/congruence

So, you can fill in the blanks as follows:

- **Blank space 28:** Angle 1
- **Blank space 29:** Angle 3
- **Blank space 30:** Angle 2
- **Blank space 31:** Angle 1
- **Blank space 32:** Angle 4
- **Blank space 33:** Angle 1
- **Blank space 34:** Angle 2
- **Blank space 35:** Angle 3
- **Blank space 36:** Angle 4

Here's the final arrangement for clarity:

| Statement | Reason |
|---------------------------------------------|------------------------------------------------|
| Line k is parallel to line m. | Given |
| Angle 1 is congruent to Angle 3. | Alternate interior angles |
| Angle 2 is supplement to Angle 1. | Linear pair |
| Angle 3 is supplement to Angle 4. | Linear pair |
| Angle 1 + Angle 2 = 180° | Definition of supplementary angles |
| Angle 3 + Angle 4 = 180° | Definition of supplementary angles |
| Since angle 3 is congruent to angle 1, then angle 2 is also congruent to angle 3. | Transitive property of equality/congruence |

This proof establishes that Angle 2 is congruent to Angle 3 using parallel lines cut by a transversal.