Question

Triangle A B C is shown with line A C is parallel to line B D.



A figure.Short description, A figure.,Long description,
The figure shows triangle A B C. The base of the triangle is line A C. At the top of the triangle is line B D, where point B is the top of the triangle.

At B, angles 1, 2, and 3 combine to form a straight line, with angle 2 being an interior angle to triangle A B C.
At A, angles 4 and 5 combine to form a straight line, with angle 5 being an interior angle to triangle A B C.
At C, angles 6 and 7 combine to form a straight line, with angle 6 being an interior angle to triangle A B C.

Question
The sum of the interior angles of a triangle equals 180 degrees.



Move options to the blanks to complete the proof.

Response area with 6 blank spaces
Statement

Reason

line A C is parallel to line B D

Given

angle 5 is congruent to
Blank space 1 empty
​and angle 6 is congruent to
Blank space 4 empty

Alternate interior angles are congruent.

the measure of angle 2 plus the measure of
Blank space 6 empty
​plus the measure of
Blank space 7 empty
equals 180 degrees

Straight angles add to 180 degrees.

the measure of angle 2 plus the measure of
Blank space 8 empty
plus the measure of
Blank space 9 empty
equals 180 degrees

Substitution

Answer 1

Here's how you can complete the proof:

- **Blank space 1**: angle 4
- **Blank space 4**: angle 7
- **Blank space 6**: angle 4
- **Blank space 7**: angle 5
- **Blank space 8**: angle 6
- **Blank space 9**: angle 5

Now let's put it all together to see the completed proof:

**Statement | Reason**
1. Line A C is parallel to line B D | Given
2. Angle 5 is congruent to angle 4 | Alternate interior angles are congruent.
3. Angle 6 is congruent to angle 7 | Alternate interior angles are congruent.
4. The measure of angle 2 plus the measure of angle 4 plus the measure of angle 5 equals 180 degrees. | Straight angles add to 180 degrees.
5. The measure of angle 2 plus the measure of angle 6 plus the measure of angle 5 equals 180 degrees. | Substitution.

This proof demonstrates that the sum of the interior angles of triangle ABC equals 180 degrees.