Constructions

LT 1B: I can copy and bisect a segment and angle. I can construct the perpendicular bisector of a line segment and construct a line parallel to a given line through a point not on the line.

2

Investigate:

• Draw a straight line segment on your paper using the straight edge given.

• How (without measuring or folding) could you copy the segment.

• Write your process on the sheet.

3

HistoryEuclidian Geometry was developed by a Roman citizen named Euclid.Euclid lived from approx. 330 to 260 BC and wrote a 13 volume book called Elements which illustrated all the concepts used in Geometric Construction

Background- Why Didn’t He Just Use a Ruler 1. They had only positive whole numbers represented by Roman numerals (I, II, III, IV, V) - no negative numbers - no fractions or decimals -no zeroSo if the line were any length other than an even answer it could not be solved in Roman culture. Example: 5 / 2= 2.52. Had no measurement system with units so a line could not be measured.As a result they had to use other tools such as a compass and straight edge.

4

Constructions

• We will learn how to do six constructions.

• For each constructions, you will show the steps in your NOTES section of your notebook.

• Then you will summarize the process underneath the diagrams in your own words.

• Make sure to write clearly and label ALL steps.

I. Copy a Segment

II. Bisect a Line Segment

III. Bisect an Angle

IV. Copy an Angle

V. Perpendicular Bisector

VI. Parallel Lines

VI. Parallel Lines