Download UNIT 1 Geometry Basic Constructions

Name_________________________________
Date
UNIT 1
Geometry
Page 2
Opening Exercise
Page 3 Definition of Circle
Pages 4-5 Basic Constructions: Practice using the Compass
Pages 6-10 Perpendicular Bisectors
Pages 11-13 Bisecting an Angle
Pages 14-15 Copying an angle
Pages 16-18 Constructing an Equilateral Triangle
Pages 19-21 Constructing an Equilateral Triangle Inscribed in a Circle
Pages 22-23 Constructing a line perpendicular to another line through a given point
Pages 24-26 Constructing a line parallel to another line through a given point
Pages 27-30 Constructing a Square Inscribed in a Circle
Page 31 Constructing a Rectangle that is not a square inside a circle
Pages 32-34 Constructing Triangle Midsegments Online Activity
Page 35 Constructing the Median of a Triangle
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Name_____________________________
Date
Opening Exercise
Materials needed: Ruler, pencil
Directions:
1.) There is a point on your paper labeled P
2.) Plot 20 points that are exactly 3 inches away from point P
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On the previous page, you should have ended up with something that either looked like a circle or was
becoming a circle. If you kept on plotting points, you would eventually have a circle.
Definition of Circle:
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Next, we are going to start CONSTRUCTIONS
What is a Construction?
Activity
Materials needed: Compass, Straight edge, pencil
Directions: Using this page and the next, construct 8 circles with each having a different radius.
Label the center point of each circle with a letter.
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Name________________________________
Date:
Opening Exercise
Plot 20 points that are exactly the same distance from both points A and B
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Name___________________________
Date:
PERPENDICULAR BISECTORS
LINE SEGMENT:
PERPENDICULAR:
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BISECTOR:
Line segment DE is bisecting line AC
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Constructing the Perpendicular Bisector of Line Segment
Activity: Using the steps below construct the perpendicular bisector of line segment AB
1.
2.
3.
4.
5.
Place the compass at one end of line segment.
Adjust the compass to slightly longer than half the line segment length.
Draw a circle with the center being the end point
Keeping the same compass width, draw a circle with the center being the other end point.
Place ruler where the circles cross, and draw the line segment.
Do the 2 circles that you drew have the same radius? _____
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Directions: Construct the perpendicular bisector of Line segment AB.
1.)Label the point where the line segments intersect as C
2.) Label the endpoints of the line you drew D and E
State 2 angles that are 90 degrees
__________ and __________
Do the 2 circles that you drew have the same radius? _____
Is point D the same distance from A that it is from B? _____
How do we know? Point D is on both circles with
centers A and B. Since the circles are equal, the radii are
equal.
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Name____________________
Date:
Bisecting an Angle
Angle:
FACTS ABOUT ANGLES
1.) Angles that are less than 90 degrees are called _____________________
2.) Angles that are Greater than 90 degrees are called ________________________
3.) Angles that EXACTLY 90 degrees are called ______________________________
4.) The three interior angles of every Triangle add up to ________________________
5.) The four interior angles of every 4 sided figure (Quadrilateral) add up to ______________
6.) A straight line is ___________________________
7.) A circle is ____________________________
8.) When two angles add up to 180 degrees, they are called ______________________________
9.) When two angles add up to 90 degrees, they are called ______________________________
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Activity: Using the steps below construct the
angle bisector of angle ABC
1.)Draw an circle that is centered at the vertex of the angle. This circle can have a radius of any length.
However, it must intersect both sides of the angle.
** We will call these intersection points P and Q . This provides a point on each line that is an equal distance
from the vertex of the angle.
2.) Draw a circle centered at point P with the same radius
3.) Draw a circle centered at point Q with the same radius
4.) Draw the bisector through the intersection point of the two circles.
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Practice Constructing the ANGLE BISECTOR
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How to Copy an angle
1.) Draw a ray that will be one of the sides of the new angle and label the end point P
2.) On the original angle, draw a circle with the center being the vertex. The circle can be any size.
However, it must intersect both sides of the angle.
3.) Draw a circle centered at the point P of the ray that you drew
4.) Using the compass, measure the opening of the original angle by placing the compass point and pencil
on the points where the circle intersects the sides
5.) Keeping the compass radius the same, put the point of the compass on the point where the circle
intersected the ray that you drew and draw a circle.
6.) Draw the other side of the angle through the intersection point of the 2 circles
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Practice copying Angles
Copy the following 2 angles
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Name__________________________________
Date:
EQUILATERAL TRIANGLES
Properties of Equilateral Triangles
1.)
2.)
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Constructing an Equilateral Triangle
**There are multiple ways to perform this construction. We will go over a couple of
them
Steps
1.) Draw a line segment of any length and label the end points A and B
2.) Place the point of the compass on point A and open up the compass so that the
other end is on point B and draw a circle
3.) Repeat step 2 with the point of the compass on Point B and draw a circle
4.) Draw two line segments connecting points A and B to the intersection point of the
circle
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Practice
Construct 2 Equilateral Triangles
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Name______________________________
Date:
Equilateral Triangle Inscribed in a Circle
We already have talked about Equilateral Triangles, but what does it mean to be “Inscribed”?
When you think of INSCRIBED, think INSIDE!
INSCRIBED –
INSCRIBED
NOT INSCRIBED
All three vertex points are not touching circle
Constructing an equilateral Triangle Inscribed in a circle
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Steps
***You may not be able to draw the entire circle for this
1.) Draw a circle of any size
2.) Keeping the same opening of the compass, place the point anywhere on the
outer edge of the circle and draw a circle
3.) Keeping the same opening of the compass, place the point of the compass on
the intersection point of your 2 circles and draw another circle
4.) Continue this process all the way around the circle until there are 6 points of
intersection on your original circle
5.) Label these points in order 1,2,3,4,5,6
6.) Use line segments to Connect points 1,3,5
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Practice
Construct an Equilateral Triangle Inscribed in a Circle
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Name__________________________
Date:
Constructing a line Perpendicular to another line through a given point
Steps
1.) Place compass on point P and draw a circle. The circle must intersect the
line segment twice. Label the two points of intersection C and D. You have
created a new line segment
2.) Construct the perpendicular bisector of line segment CD
3.) The line you draw is perpendicular to the given line segment and should go
through the given point
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Practice
Construct a line perpendicular to the given line through the given point
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Name______________________
Date:
Parallel Lines
Parallel Lines-
On a coordinate grid, parallel lines have the same slope
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Constructing a line parallel to another line through a given point
Steps
1.) Draw a line segment that goes through both segment AB and point P. Label
point C where the line you drew intersected segment AB
2.) Draw a circle with the center being point C
3.) Keeping the compass opening the same, draw a circle with the center being
point P
4.) Next we are going to copy angle PCB with point P being the vertex of our
new angle
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Practice: Construct a line parallel to the given line that goes through the given
point
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Name_________________________
Date:
Properties of Square
What is a Square?
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Constructing a Square Inscribed in a circle
Steps:
1.) Construct a circle of any size. Make sure and mark the center point
2.) Using a straight edge, draw the diameter of the circle. Label the end
points of the diameter A and B
3.) Construct the perpendicular bisector of the diameter. Label the points
where the perpendicular bisector intersects the circle C and D
4.) Connect point A, B, C, D
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Practice: On this page construct a square inscribed in a circle twice
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Challenge: Can you figure out how to construct a Rectangle inscribed in a circle.
Try it on your own
NOTE: This rectangle CAN NOT be a square
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Constructing a rectangle inscribed in a circle
Steps:
1.) Follow steps 1 thru 5 of constructing a Hexagon inscribed in a circle
2.) Connect points 1,2,4,5
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Name____________________________
Geometry
Date:
Triangle Midsegment Online Assignment
1.)
Go online and look up “Midsegment of Triangle”
Below, write down the definition of a Midsegment
How many midsegments does a triangle have? _________
What are the 2 special properties of MIDSEGMENTS?
1.)
2.)
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2.)
Label the Triangle below with points A, B, C
Research how to construct a midsegment and construct one of the
midsegments of the triangle. Label the points D and E
3.)
State 2 angles that are congruent to one another
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4.)
Triangle ABC is shown below. Construct all three midsegments
of the triangle and label the points D,E,F
5.)
After you have constructed all three midsegments, a smaller
triangle is created inside the bigger one. How do the perimeters of
the two triangles compare to each other?
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Name_____________________
Date:
Median of a triangle
Definition of Median of Triangle-
Below draw a triangle and construct All 3 medians of the triangle
The three medians of the triangle intersected at one point. What is this point called?
_________________________________
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