# Plane Figures: Two Straight Lines Crossed by a Transversal

From wikisori

## Contents

### Age

6-9.

### Materials

- Box of sticks
- Supplies
- Board covered with paper

### Preparation

### Presentation

- Place one, then another like stick on the board, having the child identify the number of straight lines on the plane.
- Then place a third stick (a different color with holes along the length) so that it crosses the other two.
- Now there are three straight lines on our plane; the third crosses the other two.
- Remove the sticks.
- Place one horizontally and tack it down reminding the child that this straight line goes on in both directions to infinity.
- Into how many parts does it divide the plane? Indicate these two parts with a sweeping hand.
- Place the second stick on the plane so that it is not parallel.
- Even this straight line goes on to infinity.
- With a black crayon, draw lines to demonstrate this.
- Identify the three parts into which the plane has been divided.
- The part of the plane which is enclosed by the two straight lines is called the internal part which we can shade in red.
- Above and below the straight lines are the external parts of the plane because they are not enclosed by these two lines.
- Place the third stick across the other two and tack it down where it intersects.
- This is a transversal (transversal < transverse: Latin trans, across, and versus, turned; thus lying crosswise).
- Two straight lines cut buy a transversal on a plane will determine a certain number of angles - how many?
- Using non-red or non-blue tacks, identify and count the angles.
- First conclusion: Two straight lines cut by a transversal will form eight angles.
- Some of these angles are lying in the internal part of the plane, while others are lying in the external part.
- Remove the tacks.
- Identify and count the angles in the internal part, using red tacks (same color as the plane).
- These four angles are interior angles because they lie in the internal part of the plane.
- Do the same, identifying the exterior angles.
- The four angles are exterior angles because they lie in the external part of the plane.

**Second presentation:**

Two straight lines cut by a transversal form four interior and four exterior angles.

- We need to divide these eight angles according to different criteria.
- Remove the red and blue tacks and identify two new groups using two other colors: four angles formed by one straight line and a transversal; and four angles formed by the other straight line and a transversal.
- All of the work that we'll be doing involves pairing an angle from one group with an angle from another group.
- We won't be working with two angles from the same group because that would mean only two straight lines were being considered, not three.
- Let's examine these pairs.
- Remove the tacks.
- Using two tacks of the same color, the teacher identifies two angles.
- These two angles are a pair of alternate angles.
- Recall the meaning of alternate.
- One is on one side; the other is on the the other side of the transversal.
- On what part of the plane are they? Internal, therefore they are also interior angles.
- We combine these two characteristics into one name: alternate interior angles.
- Invite the child to identify the other pair with two tacks of a different color.
- The child draws these and labels them.
- Remove the tacks.
- The directress identifies another pair of angles.
- These are a pair of angles that lie on the same side of the transversal.
- On what part of the plane do they lie? Internal, therefore they are also interior angles.
- We can call these interior angles that lie on the same side of the transversal.
- Invite the child to identify another pair with two tacks of a different color.
- The child draws the angles and labels them appropriately.
- Remove the tacks.
- The directress identifies another pair of angles.
- These are alternate angles because they lie on on one side one on the other side of the transversal.
- The child identifies in what part of the plane they lie - external - and their corresponding name - exterior.
- These are alternate exterior angles.
- Invite the child to look for another pair and identify them with two tacks of a different color.
- The child draws the situation and labels it accordingly.
- Remove the tacks.
- The directress identifies two angles.
- These are a pair of angles that lie on the same side of the transversal.
- The child identifies in which part of the plane they lie - external - and recalls their subsequent name - exterior.
- Therefore these angles can be called exterior angles that lie on the same side of the transversal.
- The child is invited to identify another pair using two tacks of a different color.
- The child copies this situation and labels it.
- Remove the tacks.
- This time an exterior angle will be paired in a relationship with an interior angle.
- The child chooses an angle, identifying it with a tack.
- The other angle must be formed by the other straight line, as you remember, so that three lines will be involved.
- The directress identifies the other angle of the pair.
- These are corresponding angles, because they follow a certain order.
- Both angles lie on the same side of the transversal, and each angle lies above its straight line.
- Invite the child to identify other pairs using different color tacks for each pair of angles.
- All eight angles are used.
- The child copies the situation and labels it accordingly.
- Note: These angles have only one quality, since the pair is divided among the two different parts of the plane.
- Finish with classified nomenclature and commands.
- A command might ask the child to identify the other member of a given pair of angles.

### Control Of Error

### Points Of Interest

### Purpose

### Variation

### Links

### Handouts/Attachments