Aim #7: How do we do construct equilateral triangles?
CCGeometry 10 R
Do Now Fill in the blanks:
Line Segment connecting points A and B is the set consisting of A, B,
• The ______________
and all points on the line AB between A and B.
Circle
• Given a point C in a plane and a number r > 0, the ____________
with center C
and radius r is the set of all points in the plane that are distance r from the
point C.
Radius
• A segment from the center of a circle to a point on the circle is a __________.
Equilateral
• An ________________
triangle has all sides of equal length.
Collinear
• ______________
points are points that lie on the same line.
Collinear
Non - _______________
• _____
points are points that do not line on the same line.
Length
• The __________
of segment AB is the distance from A to B.
Standard Notation we will use in this course
AB or "ray AB" : A ray with vertex A that contains the point B.
AB or "line AB" : a line that contains points A and B.
AB or "segment AB" : A segment with endpoints A and B.
AB : The length of segment AB.
Geometric construction: drawing of figures in the plane, based on geometric
conditions, using only a compass and straightedge.
You need a working compass and a straightedge.
Margie has three cats. She has heard that cats in a room position themselves at
equal distances from one another, and wants to test that theory. Margie notices
that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her
Siamese, is lying on her desk chair (at J). If the theory is true, where will she find
Mack, her calico cat? Use the scale drawing of Margie‛s room shown below,
together with only a compass and straightedge. Place an M where Mack will be if
the theory is true.
m
All CONSTRUCTIONS must be done using a compass and straightedge.
CONSTRUCTION (1): Construct an equilateral triangle.
Steps:
[When drawing a circle(arc),
specify its center and radius.]
c
A
B
n
Exercises
1. Construct an equilateral triangle with side length n.
n
m.
2. Construct an equilateral triangle with side length
0
3. Construct a 60 angle.
2m.
4. Construct an equilateral triangle with side length
m
5. Construct three equilateral triangles, where the first and second triangles share
a common side, and the second and third triangles share a common side.
6. Construct a regular hexagon.
Hint: Draw the three diagonals. What do you notice?
Let's Sum it Up!!
http://www.mathopenref.com/equilateral.html
What does the clip demonstrate about an equilateral triangle?
http://www.mathopenref.com/constequilateral.html
How do we know the three sides are congruent?
How do we know the triangle is equilateral?