Plane Figures: Two Straight Lines Crossed by a Transversal

Age
6-9.

Materials

 * Box of sticks
 * Supplies
 * Board covered with paper

Presentation

 * 1) Place one, then another like stick on the board, having the child identify the number of straight lines on the plane.
 * 2) Then place a third stick (a different color with holes along the length) so that it crosses the other two.
 * 3) Now there are three straight lines on our plane; the third crosses the other two.
 * 4) Remove the sticks.
 * 5) Place one horizontally and tack it down reminding the child that this straight line goes on in both directions to infinity.
 * 6) Into how many parts does it divide the plane? Indicate these two parts with a sweeping hand.
 * 7) Place the second stick on the plane so that it is not parallel.
 * 8) Even this straight line goes on to infinity.
 * 9) With a black crayon, draw lines to demonstrate this.
 * 10) Identify the three parts into which the plane has been divided.
 * 11) The part of the plane which is enclosed by the two straight lines is called the internal part which we can shade in red.
 * 12) Above and below the straight lines are the external parts of the plane because they are not enclosed by these two lines.
 * 13) Place the third stick across the other two and tack it down where it intersects.
 * 14) This is a transversal (transversal &lt; transverse: Latin trans, across, and versus, turned; thus lying crosswise).
 * 15) Two straight lines cut buy a transversal on a plane will determine a certain number of angles - how many?
 * 16) Using non-red or non-blue tacks, identify and count the angles.
 * 17) First conclusion: Two straight lines cut by a transversal will form eight angles.
 * 18) Some of these angles are lying in the internal part of the plane, while others are lying in the external part.
 * 19) Remove the tacks.
 * 20) Identify and count the angles in the internal part, using red tacks (same color as the plane).
 * 21) These four angles are interior angles because they lie in the internal part of the plane.
 * 22) Do the same, identifying the exterior angles.
 * 23) 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.


 * 1) We need to divide these eight angles according to different criteria.
 * 2) 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.
 * 3) All of the work that we'll be doing involves pairing an angle from one group with an angle from another group.
 * 4) 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.
 * 5) Let's examine these pairs.
 * 6) Remove the tacks.
 * 7) Using two tacks of the same color, the teacher identifies two angles.
 * 8) These two angles are a pair of alternate angles.
 * 9) Recall the meaning of alternate.
 * 10) One is on one side; the other is on the the other side of the transversal.
 * 11) On what part of the plane are they? Internal, therefore they are also interior angles.
 * 12) We combine these two characteristics into one name: alternate interior angles.
 * 13) Invite the child to identify the other pair with two tacks of a different color.
 * 14) The child draws these and labels them.
 * 15) Remove the tacks.
 * 16) The directress identifies another pair of angles.
 * 17) These are a pair of angles that lie on the same side of the transversal.
 * 18) On what part of the plane do they lie? Internal, therefore they are also interior angles.
 * 19) We can call these interior angles that lie on the same side of the transversal.
 * 20) Invite the child to identify another pair with two tacks of a different color.
 * 21) The child draws the angles and labels them appropriately.
 * 22) Remove the tacks.
 * 23) The directress identifies another pair of angles.
 * 24) These are alternate angles because they lie on on one side one on the other side of the transversal.
 * 25) The child identifies in what part of the plane they lie - external - and their corresponding name - exterior.
 * 26) These are alternate exterior angles.
 * 27) Invite the child to look for another pair and identify them with two tacks of a different color.
 * 28) The child draws the situation and labels it accordingly.
 * 29) Remove the tacks.
 * 30) The directress identifies two angles.
 * 31) These are a pair of angles that lie on the same side of the transversal.
 * 32) The child identifies in which part of the plane they lie - external - and recalls their subsequent name - exterior.
 * 33) Therefore these angles can be called exterior angles that lie on the same side of the transversal.
 * 34) The child is invited to identify another pair using two tacks of a different color.
 * 35) The child copies this situation and labels it.
 * 36) Remove the tacks.
 * 37) This time an exterior angle will be paired in a relationship with an interior angle.
 * 38) The child chooses an angle, identifying it with a tack.
 * 39) The other angle must be formed by the other straight line, as you remember, so that three lines will be involved.
 * 40) The directress identifies the other angle of the pair.
 * 41) These are corresponding angles, because they follow a certain order.
 * 42) Both angles lie on the same side of the transversal, and each angle lies above its straight line.
 * 43) Invite the child to identify other pairs using different color tacks for each pair of angles.
 * 44) All eight angles are used.
 * 45) The child copies the situation and labels it accordingly.
 * 46) Note: These angles have only one quality, since the pair is divided among the two different parts of the plane.
 * 47) Finish with classified nomenclature and commands.
 * 48) A command might ask the child to identify the other member of a given pair of angles.