Aim #7: How do we do construct equilateral triangles?
CC Geometry H
Do Now Fill in the blanks:
• The ______________ connecting points A and B is the set consisting of A, B,
and all points on the line AB between A and B.
• 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.
• A segment from the center of a circle to a point on the circle is a __________.
• An ________________ triangle has all sides of equal length.
• ______________ points lie on the same line.
• _____ - _______________ points are points that do not line on the same line.
• __________ of a 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: a set of instructions for drawing points, lines, circles,
and figures in the plane.
You will need a 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
Write your own set of steps to construct an equilateral triangle.
[When drawing a circle, specify its center and radius.]
A
B
Exercises
m
n
1a) Copy segment n in the space below.
n
working line ray
b) Construct segment n + m in the space below.
m
n
m.
2. Construct an equilateral triangle with side length
m
m
m
0
3. Construct a 60 angle using segment n.
60
n
2m.
4a) Construct an equilateral triangle with side length
m
m
b) Clearly and precisely list the steps needed to accomplish this construction.
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. Clearly and
precisely list the steps needed to accomplish this construction.
Steps
1. Draw AB.
2. Draw circle A, radius AB.
3. Draw circle B, radius AB.
4. Label the intersection points of
the 2 circles as C and D.
5. Draw circle C, radius CB.
6. Label the intersection pt. of
circles C and B as E.
7. Draw all congruent (equal)
segments to AB between the
labeled points.
6. Why are circles so important in the construction of equilateral triangles?
The radius of equal sized circles doesn't change. Guarantees that all 3 side lengths of the triangle are equal.
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?
CC Geometry H
Name ______________________
HW #7
Date________________
1. You will need a compass and straightedge.
Cedar City boasts two city parks and is in the process of designing a third. The
planning committee would like all three parks to be equidistant from one another to
better serve the community. A sketch of the city appears below, with the centers
of the existing parks labeled as P1 and P2 . Identify two possible locations for the
third park and label them as P3a and P3b on the map. Clearly and precisely list the
mathematical steps used to determine each of the two potential locations.
2. Construct an equilateral triangle using the length of P1 P2 as a side.
OVER
3. Use the skills you developed in Aim 7 to construct a regular hexagon.
Review
4. In the diagram below, find x, y and m≮AGD.
0
5a) If BC bisects ≮DBA and m≮DBC = 25 , find m≮DBA.
D
C
1
B
2
A
b) If BC bisects ≮DBA with m≮DBA = 6x - 8 and m≮1 = 2x + 6, find x and m≮2.