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# This paper folding activity reveals the angle relationships of parallel lines

Subject:

Math

Grades:

9, 8, 10

Title – Angle Relationships and Parallel Lines

By – Pam Bailey

Primary Subject – Math

Grade Level – 8-10

Review:

- Labeling angles
- Congruent angles
- Supplementary angles

Materials:

- lined notebook paper — 2 per person
- Rulers
- Scissors

Objective: Students will discovery the angle relationships of parallel lines by completing a paper folding activity.

Procedures:

- 1. Fold paper in half vertically and crease. While paper is folded in this “hot dog” style, fold it once more along the pink margin line. When paper is unfolded there should be three creases.

- 2. Using a ruler draw a vertical line along the middle crease — transversal. (The outside fold lines are an aid in drawing parallel lines.)

- 3. Fold paper in half horizontally in the “hamburger” style and crease. Unfold paper.

- 4. Draw Parallel Lines — On the top half of the paper, left of the transversal, place a point at the intersection of a blue line and the left hand crease. Your choice which line is chosen. Label point as point A.

- 5. Count down from pt. A ______ number of lines. Follow this line to the right hand crease and place another point. Label the right hand point as point B. Use ruler to connect points to form line AB.

- 6. On the bottom half of the paper, left of the transversal, place a point at the intersection of a blue line and the left hand crease. Label point as point C.

- 7. Count down the same number of lines that you chose on step 5. Follow this line to the right hand crease and place another point. Label the right hand point as point D. Use a ruler to connect points to form line CD.

- 8. Number angles 1-4 down the left hand side of the transversal and 5-8 down the right hand side of the transversal.

- 9. The angles in the gray areas are called exterior angles because they are outside of the parallel lines.

- The angles in the white area are called interior angles because they are between the parallel lines.

- 10. Use scissors to cut along the transversal, both parallel lines, and the hamburger crease.

- 11. Using the cut out angle pieces fill in the chart by determining which angles are congruent.

NAME____________________________________

Note: you may wish to reconstruct your original paper to help determine location.

CONGRUENT ANGLES | Use the following terms to describe the location of the angles: transversal, parallel lines, intersecting lines, interior angles, and exterior angles | Angle Relationships – TYPES |

1. | ||

2. | ||

3. | ||

4. | ||

5. | ||

6. | ||

7. | ||

8. | ||

9. | ||

10. | ||

11. | ||

12. |

Use the line below to help determine which angles are supplementary or a linear pair.

____________________________________________

Angles that are SUPPLEMENTARY or a LINEAR PAIR | Use the following terms to describe the location of the angles: transversal, parallel lines, intersecting lines, interior angles, and exterior angles | Angle Relationships – TYPES |

1. | ||

2. | ||

3. | ||

4. | ||

5. | ||

6. | ||

7. | ||

8. | ||

9. | ||

10. | ||

11. | ||

12. |

Use charts on pages 2 and 3 to help answer the following. (Note: *ANGLES ARE NUMBERED IN THE SAME ORDER AS BEFORE)*.

I. m**<1** = 2x+5 m**<5** = 75

- a) State the relationship between the angles._____________________

- b) Determine the value of x.

- c) Find all angle measures.

II. m**<1**=5x-3 m**<5**=97

- a) State the relationship between the angles. ______________________

- b) Determine the value of x.

- c) Find all angle measures.

III. m**<2**=2x-90 m**<7**=x+15

- a) State the relationship between the angles. ______________________

- b) Determine the value of x.

- c) Find all angle measures.

IV. m**<6**=7x-75 m**<8**=4x-15

- a) State the relationship between the angles. ______________________

- b) Determine the value of x.

- c) Find all angle measures.

V. m**<3**=2(x+5) m**<8**=3x-13

- a) State the relationship between the angles. ______________________

- b) Determine the value of x.

- c) Find all angle measures.

VI. m**<2**=x+7 m**<3**=5x+41

- a) State the relationship between the angles. ______________________

- b) Determine the value of x.

- c) Find all angle measures.

*(Include graphic here: ANGLES ARE NUMBERED, GOING DOWN THE LEFT SIDE OF THE TRANSVERSAL AS 5, 1, 8, AND 6. GOING DOWN THE RIGHT SIDE OF THE TRANSVERSAL THE ANGLES ARE NUMBERED AS 3, 7, 4, AND 2.)*

NAME___________________________________________

State which angles illustrate the following relationships.

1. Corresponding angles

2. Alternate Interior Angles

3. Alternate Exterior Angles

4. Vertical Angles

5. Same Side Interior Angles

6. Linear Pair

7. Supplementary Angles

FIND x.

8. m**<6**=-2x+35 m**<3**=x-22

9. m**<4**=-x+25 m**<7**=5x+23

E-Mail Pam Bailey!