CCGSP Analytic Geometry
Unit 1 Section 1 – Day 3
Warm Up:
Name:___________________________
For the function f(x) = -5x – 3, find f(1).
LEQ: How can I use a straight edge and a compass to copy and bisect both lines and angles?
Historical Connection
The study of Geometry was born in Ancient Greece, where mathematics was thought to be
embedded in everything from music to art to the governing of the universe. Plato, an ancient
philosopher and teacher, had the statement, “Let no man ignorant of geometry enter here,” placed at
the entrance of his school. This illustrates the importance of the study of shapes and logic during that
era. Everyone who learned geometry was challenged to construct geometric objects using two simple
tools, known as Euclidean tools:


A straight edge without any markings (used to construct lines)
A compass (used to construct circles)
As geometry grew in popularity, math students and mathematicians would challenge each other to
create constructions using only these two tools. Some constructions were fairly easy (Can you
construct a square?), some more challenging, (Can you construct a regular pentagon?), and some
impossible even for the greatest geometers (Can you trisect an angle? In other words, can you
divide an angle into three equal angles?). Archimedes (287-212 B.C.E.) came close to solving the
trisection problem, but his solution used a marked straight edge. What constructions can you create?
Task 1: Copy a Line Segment
http://www.mathopenref.com/constcopysegment.html
1)
Give two names for the segment below ___________ and
2)
Construct another line segment the same length as, beginning at point C.
A
____________
●
C
B
3)
Line Segments are named by the endpoints. Draw point D, so that is the other endpoint of the
new segment. Complete the statement: ______ ≅ ______
4)
You try: Construct a line segment the same length, beginning at point P.
M
●
P
L
Complete the statement ______ ≅ ______
Task 2: Copy an Angle
5)
http://www.mathopenref.com/constcopyangle.html
Construct a copy of the angle at the new point.
6) Give three names for
the given angle.
___________
___________
___________
●
D
7)
Why would you use three letters to name an angle, when you can just use one? When would
it be useful to use the three letter name?
8)
You try: Construct a copy of the angle below at the new point.
●
M
Complete the statement ______ ≅ ______
Task 3: Construct the perpendicular bisector of a line segment
http://www.mathopenref.com/constbisectline.html
9) Construct the perpendicular bisector of ̅̅̅̅
𝐴𝐵
10) Complete the statements:
__________ bisects ___________
________ ≅ ________
________ ≅ ________
m<______ = __________
m<______ = __________
11)
̅̅̅̅. Mark all congruent segments and angles.
You try: Construct the perpendicular bisector of 𝐴𝐵
Task 4: Construct the bisector of an angle
http://www.mathopenref.com/constbisectangle.html
13) Complete the statements:
12) Construct the angle bisector of
__________ bisects ___________
________ ≅ ________
m<_________ = ½ (__________)
m<_________ = 2( __________)
14)
You try: Construct the perpendicular bisector of ̅̅̅̅
𝐴𝐵 . Mark all congruent angles.
15) Think-Pair-Share: Compare and Contrast a line, a line segment, and a ray. Use the table
below to organize your thoughts.
Definition
Line
Line
Segment
Ray
.
Notation