E6 Students will be expected to recognize, name, describe, and represent perpendicular lines/segments, bisectors of angles and segments, and perpendicular-bisectors of segments.  

What are the characteristics of a ‘line’ in geometry? A line is straight and extends in both directions forever. It has no definite endpoints.

What defines a ‘line segment’ in geometry? B A line segment is straight and has two definite endpoints. This is line segment AB or BA.

What are perpendicular lines? Where do we see perpendicular lines in the real world?

Student Activities How can you use a mira to draw perpendicular lines? Draw a line segment and place the mira across it, moving the mira until the image of the part of the segment on one side of the mira falls on the segment on the other side. The line on which the mira sits is perpendicular to the original line; therefore, place a pencil against the beveled edge of the mira and draw in this perpendicular.

What does ‘bisect’ mean? ‘Bisect’ means to divide in half. What can be bisected in geometry? Line segments and angles can be bisected.

A perpendicular-bisector is a line segment that cuts through a second segment or line forming right angles. It also cuts the segment in half or bisects it. Try to use your mira to show a perpendicular-bisector. Explanation: When the image of the endpoint of the segment falls on the other endpoint, the mira is bisecting the segment; therefore, the line on which the mira sits would be the perpendicular-bisector of the segment.

What are parallel lines? Where do we see parallel lines in the real world?

Use two straws to make the following arrangements: parallel to one another intersecting perpendicular at an end point of one straw perpendicular at endpoints of each straw one straw perpendicular to the other straw at its midpoint one straw bisecting the other straw but not perpendicular each straw bisecting the other straw but not perpendicular one straw bisected by the other straw and perpendicular each straw bisecting the other straw and perpendicular

Bisecting Angles Using Three Methods Bisect the first angle given to you by folding one arm onto the other. Bisect the next angle by using a mira to find where one arm would reflect onto the other when it is placed through the vertex Bisect the third angle by using a protractor to measure the angle. Then bisect it. Practise the three methods by bisecting the other angles on the sheet provided to you.  

E6. 1 Draw a right angle, an acute angle, and an obtuse angle E6.1 Draw a right angle, an acute angle, and an obtuse angle. Use only a mira to draw in the bisector of each angle. Check your results by paper folding and by measuring the angles with a protractor.

E6. 2 Use the capital letters of the alphabet that use only segments E6.2 Use the capital letters of the alphabet that use only segments. Find examples of bisectors of segments, perpendicular segments, and perpendicular-bisectors. Share your findings.

E6.3 Draw, without measuring, a segment that is approximately 10cm long. Next, construct a perpendicular bisector of this segment, using only a mira.

E6. 4 Fold sheets of paper in half and then in half again E6.4 Fold sheets of paper in half and then in half again. Open them up to reveal the folds and draw in segments along these folds. Describe the relationship between these two segments.