Geometry Workbook 1: Vocabulary, Geometric Objects and Their Symbols, and Geometric Constructions Student Name __________________________________________ STANDARDS: G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. SKILLS: I will be able to define any geometric term using words, diagrams, and notation. I will be able to explain what the undefined terms are and why they are undefined. I will be able to use geometric concepts to establish a rationale for the steps/procedures used in performing a construction. I will be able to use a compass and straightedge to create the following constructions. o Copy a given line segment. o Copy a given angle. o Bisect a line segment. o Bisect an angle. o Construct a line perpendicular to a given line through a point on that line. o Construct a line perpendicular to a given line through a point not on that line. o Construct the perpendicular bisector of a line segment. o Construct a line parallel to a given line through a point not on the line. o Construct geometric figures using a variety of tools and methods. I will be able to construct the following: o An equilateral triangle inscribed in a circle. o A square inscribed in a circle. o A regular hexagon inscribed in a circle I will be able to construct the following: o An equilateral triangle o A square o A regular hexagon
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Geometry Workbook 1 - Union Parish School DistrictGeometry Workbook 1: Vocabulary, Geometric Objects and Their Symbols, and Geometric Constructions Student Name _____ STANDARDS: G.CO.A.1
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Geometry Workbook 1:
Vocabulary, Geometric Objects and Their Symbols, and
Geometric Constructions
Student Name __________________________________________
STANDARDS:
G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
G.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
SKILLS:
I will be able to define any geometric term using words, diagrams, and notation.
I will be able to explain what the undefined terms are and why they are undefined.
I will be able to use geometric concepts to establish a rationale for the steps/procedures used in
performing a construction.
I will be able to use a compass and straightedge to create the following constructions. o Copy a given line segment. o Copy a given angle. o Bisect a line segment. o Bisect an angle. o Construct a line perpendicular to a given line through a point on that line. o Construct a line perpendicular to a given line through a point not on that line. o Construct the perpendicular bisector of a line segment. o Construct a line parallel to a given line through a point not on the line. o Construct geometric figures using a variety of tools and methods.
I will be able to construct the following: o An equilateral triangle inscribed in a circle. o A square inscribed in a circle. o A regular hexagon inscribed in a circle
I will be able to construct the following: o An equilateral triangle o A square o A regular hexagon
G.CO.D.12 STUDENT NOTES & PRACTICE WS #1β geometrycommoncore.com 1
1. Copying a segment
(a) Using your compass, place the pointer at Point A and extend it until it reaches Point B. Your compass now has the measure of AB.
(b) Place your pointer at Aβ, and then create the arc using your compass. The intersection is the same radius, thus the same distance as AB. You have copied the length AB.
NYTS (Now You Try Some)
Copy the given segment.
Create the length 3AB
2. Bisect a segment
(a) Given AB (b) Place your pointer at A, extend your compass so that the distance exceeds half way. Create an arc.
(c) Without changing your compass measurement, place your point at B and create the same arc. The two arcs will intersect. Label those points C and D.
(d) Place your straightedge on the
paper so that it formsπΆπ· β‘ . The
intersection of πΆπ· β‘ and π΄π΅Μ Μ Μ Μ is the
bisector of π΄π΅Μ Μ Μ Μ .
(e) I labeled it M, because it is the midpoint of π΄π΅Μ Μ Μ Μ .
A B
B'A B
A'
A B A'
A B A'
A
B
A
B
D
C
A
B
M
D
C
A
B M
A
B
G.CO.D.12 STUDENT NOTES & PRACTICE WS #1β geometrycommoncore.com 2
NYTS (Now You Try Some)
Bisect the segment (find the midpoint).
3. Copy an angle
(a) Given an angle and a ray. (b) Create an arc of any size, such that it intersects both rays of the angle. Label those points B and C.
(c) Create the same arc by placing your pointer at Aβ. The intersection with the ray is Bβ.
(d) Place your compass at point B and measure the distance from B to C. Use that distance to make an arc from Bβ. The intersection of the two arcs is Cβ.
(e) Draw the ray π΄β²πΆβ² . (f) The angle has been copied.
NYTS (Now You Try Some)
Copy the given angle.
A
B C
D
A
A'
C
A
A'
B
B'
C
A
A'
B
C'
B'
C
A
A'
B
C'
B'
C
A
A'
B
o
o
C'
B'
C
A
A'
B
A A'
G.CO.D.12 STUDENT NOTES & PRACTICE WS #1β geometrycommoncore.com 3
4. Construct a line parallel to a given line through a point not on the line.
(a) Given a point not on the line. (b) Place your pointer at point B and measure from B to C. Now place your pointer at C and use that distance to create an arc. Label that intersection D.
(c) Using that same distance, place your pointer at point A, and create an arc as shown.
(d) Now place your pointer at C, and measure the distance from C to A. Using that distance, place your pointer at D and create an arc that intersects the one already created. Label that point E.
(e) Create π΄πΈ β‘ . (f) π΄πΈ β‘ is parallel to
NYTS (Now You Try Some)
Find the parallel line though the point not on the line.
B C
A
DB C
A
DB C
A
E
DB C
A E
DB C
A E
DB C
A
G.CO.D.12 GUIDED PRACTICE WS #1β geometrycommoncore.com 1
1. Copying a segment
Copy the given segment.
Create the length 3AB
Create the length AB β CD
2. Bisect a segment (find the midpoint)
3. Copy an angle
A B A'
A B A'
A B
C D
A
B C
D
A A'
G.CO.D.12 GUIDED PRACTICE WS #1β geometrycommoncore.com 2
4. Construct a line parallel to a given line through a point not on the line.
4. Given ABC, can you think of a way to create a line parallel to AB through point C?
(Hint: How could copying an angle help you?)
5. Create a parallel line to π·πΈ β‘ through point F.
BC
A
D F
E
G.CO.D.12 STUDENT NOTES & PRACTICE WS #2β geometrycommoncore.com 1
1. Construct the perpendicular bisector of a line segment
(a) Given AB (b) Place your pointer at A, extend your compass so that the distance exceeds half way. Create an arc.
(c) Without changing your compass measurement, place your point at B and create the same arc. The two arcs will intersect. Label those points C and D.
(d) Place your straightedge on the
paper and create πΆπ· β‘ . (e) πΆπ· β‘ is the perpendicular bisector of π΄π΅Μ Μ Μ Μ .
NYTS (Now You Try Some)
Construct the perpendicular bisector.
A
BA
B
D
C
A
B
M
D
C
A
B
M
D
C
A
B
A
B CD
G.CO.D.12 STUDENT NOTES & PRACTICE WS #2β geometrycommoncore.com 2
2. Construct a line perpendicular to a given segment through a point on the line.
(a) Given a point on a line. (b) Place your pointer at point A. Create arcs equidistant from A on both sides using any distance. Label the intersection points B and C.
(c) Place your pointer on point B and extend it past A. Create an arc above and below point A.
(d) Place your pointer on point C and using the same distance, create an arc above and below A. Label the intersections as points D and E.
(e) Create DE . f) DE is perpendicular to the line through A.
NYTS (Now You Try Some)
Construct the perpendicular line through a point on the line.
AC A B C A B
E
D
C A B
E
D
C A B
E
D
C A B
G.CO.D.12 STUDENT NOTES & PRACTICE WS #2β geometrycommoncore.com 3
3. Construct a line perpendicular to a given line through a point not on the line.
(a) Given a point A not on the line. (b) Place your pointer on point A, and extend It so that it will intersect with the line in two places. Label the intersections points B and C.
(c) Using the same distance, place your pointer on point C and create an arc on the opposite side of point A.
(d) Do the same things as step (c) but place your pointer on point B. Label the intersection of the two arcs as point D.
(e) Create π΄π· β‘ . (f) π΄π· β‘ is perpendicular to the given line through point A.
NYTS (Now You Try Some)
Construct the perpendicular line through a point not on the line.
A
CB
A
CB
A
D
CB
A
D
CB
A
D
CB
A
G.CO.D.12 STUDENT NOTES & PRACTICE WS #2β geometrycommoncore.com 4
4. Bisect an angle
(a) Given an angle. (b) Create an arc of any size, such that it intersects both rays of the angle. Label those points B and C.
(c) Leaving the compass the same measurement, place your pointer on point B and create an arc in the interior of the angle.
(d) Do the same as step (c) but place your pointer at point C. Label the intersection D.
(e) Create AD . AD is the angle bisector.
(f) AD is the angle bisector.
NYTS (Now You Try Some)
Bisect the angle.
A
C
A
B
C
A
B
D
C
A
B
D
C
A
B
o
oD
C
A
B
G.CO.D.12 GUIDED PRACTICE WS #2β geometrycommoncore.com 1
1. Construct the perpendicular bisector of a line segment
2. Construct a line perpendicular to a given segment through a point on the line.
3. Construct a line perpendicular to a given line through a point not on the line.
A
B CD
G.CO.D.12 GUIDED PRACTICE WS #2β geometrycommoncore.com 2
Construct a Midpoint Construct a Perpendicular Line
Through a Point Not on the Line Construct a Perpendicular Line
Through a Point On the Line
Construct an Angle Bisector
1. When performing these constructions you kept your compass at a fixed length. This creates distances that are equal - thus the 4 equal sides of a rhombus. a) Use a ruler and draw in the missing sides of the rhombus in each of these constructions. b) Shade the rhombus with your pencil.
2. In the first three constructions we needed to create lines that were perpendicular.
Which property of a rhombus do you think we are using to accomplish this goal?
Opposite sides are || Diagonals bisect each other
Opposite sides are Diagonals are
Opposite angles are Diagonals are Bisectors
Consecutive βs = 180
3. In the angle bisector construct we need to divide an angle into two equal parts.
Which property of a rhombus do you think we are using to accomplish this goal?