Fun with angles

This lesson plan will help the students visualize the different angles (corresponding, alternate interior, and same-side interior) when coplanar lines are cut by a transversal.

A lesson plan for grades 7–8 Mathematics

By Scott Black

Provided by Teachers Connect

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Related topics

• Learn more about alternate interior angles, angles, corresponding angles, geometry, interior angles, mathematics, and same-side interior angles.

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Learning outcomes

To help the students visualize the different angles (corresponding, alternate interior, and same-side interior) when coplanar lines are cut by a transversal.

Teacher planning

Time required for lesson

30 minutes

Materials/resources

• Ruler
• paper
• optionl: overhead and transparencies of Diagram 1, Diagram 2, Diagram 3, and Diagram 4

Pre-activities

• Copy diagrams 1 and 2 on the board and give students the standard definition of corresponding, alternate interior, and same-side interior angles and point them out.
• Corresponding angles are angles in the same place relative to the transversal and lines being intersected (examples: angles 1 and 5, 2 and 6, 3 and 7, 4 and 8).
• Interior angles are the angles between the two coplanar lines being intersected by the transversal. (examples: angles 3, 4, 5, and 6).
• Alternate interior angles are non-adjacent interior angles on different sides of the transversal. (examples: angles 3 and 6, 4 and 5).
• Same-side interior angles are interior angles on the same side of the transversal. (examples: angles 3 and 5, 4 and 6).

Activities

1. Have students copy diagrams 1 and 2 on their paper by using a ruler. Trace on top and bottom of the ruler to get the coplanar lines a and b. Next use the ruler to help draw the transversal t that intersects both a and b.
   Hint: When tracing out the following interior angles, only trace the part of the transversal that is between the two lines being cut.
2. Have the students trace out the alternate interior angles 3 and 6 found on diagram 1. Ask them: “Do these angles form a particular shape?” Response should be they look they a Z shape.
3. Now have them trace out angles 4 and 5 on the same diagram. Now ask: “Do they form the same type of shape?” These two will form a backwards Z shape.
4. Repeat the above using diagram 2. Have them trace out angles 3 and 6. Ask: “Do these form a particular shape?” Should resemble a N shape. Repeat with angles 4 and 5. Ask: “Do these form the same shape?” These two angles will give a N shape that have been flipped.
5. Next have them trace out the same-side interior angles 4 and 6 on diagram 1. Ask: “What type of shape do they form?” Should resemble a C shape. Repeat with angles 3 and 5. Ask: “Do they form a similar shape?” These two form a backwards C shape.
6. Now repeat by using diagram 2. Trace out the same-side interior angles 4 and 6. Ask: “What shape do they form?”. These form a U shape. Repeat with angles 3 and 5. Ask: ” Do they form a similar shape?” These form a U shape that has been flipped.
7. Have the students trace out the corresponding angles 4 and 8 in diagram 1. Ask: “Do these angles form a particular shape?” Should resemble a F shape. Repeat with angles 3 and 7. Ask: “Do these angles form the same type of shape?” They form a F shape that is turned backwards. Can repeat with other examples of corresponding angles from diagram 1 and 2 and they all resemble a F shape that has been flipped or turned a certain way.
8. WRAP UP: Copy down the shapes of the corresponding angles, alternate interior angles, and same-side interior angles found in diagram 3. Point out to the students that if the traced out angles fit into one of the three categories then it is either corresponding if it resembles a F shape, alternate interior if it resembles a N or Z shape, and same-side interior if it resembles a U or C shape. If it does not fit into one of these categories, then it is not one of these pairs of angles.

Assessment

For a quick check before the homework assignment copy diagram 4 on the board and have the students identify the below pairs of angles as corresponding angles, alternate interior angles, same-side interior angles, or none of these.

1. angles 1 and 3
2. angles 7 and 12
3. angles 14 and 15
4. angles 4 and 14
5. angles 10 and 15
6. angles 7 and 10
7. angles 8 and 16
8. angles 6 and 10

Answers:

1. corresponding
2. alternate interior
3. same-side interior
4. none
5. alternate interior
6. none
7. corresponding
8. same-side interior.

You can use other pairs of angles in diagram if you need to continue the practice.

Supplemental information

Ray C. Jurgensen, Richard Brown, and John Jurgensen, Geometry, Houghton Mifflin Co., 1992, p. 74.

Comments

This lesson plan is from the collection of the Tried *n* True lesson plans from the Department of Public Instruction.