HARNETT COUNTY HIGH SCHOOLS
Course:
Geometry
Title of Unit: Transformations and Similarity
Timeframe:
4 – 5 days
Content Area Standard(s): CO.2, C.1, MG.3, SRT.1, SRT.2, SRT.3,
SRT.4, SRT.5,
Reading Standard(s): 3, 4, 5, 7, 9
Writing Standard(s):
1, 4, 5, 10
Math Practice(s):
3, 6, 7
Technology Standard(s): HS.TT.1.1, HS.RP.1.1, HS.SE.1.1,
HS.S1.1.1
Learning Experiences: The learner will discuss and learn dilations and
compare them to reflections, also will investigate how dilations affect
lines and line segments. The learner will also prove theorems about
proportions in triangles and to demonstrate how all circles are similar.
The learner will see how similarity can be used to solve a variety of
mathematics and real world problems.
Project Goals and Description of Unit:
Essential Questions:
What are the key properties of dilations? (5-1)
How do you draw the image of a figure under dilation? (5-2)
What does it mean for two figures to be similar? (5-3)
What can you conclude about similar triangles and how can you prove
triangles are similar? (5-4)
How can you use similar triangles and similar rectangles to solve
problems? (5.5)
How does a line that is parallel to one side of a triangle divide the two
sides that it intersects? (5-6)
How can you use triangle similarity to prove the Pythagorean Theorem?
(5-7)
Vocabulary: center of dilation (5-1), dilation (5-1), scale factor (5 – 1),
similar (5 – 3), similarity transformation (5 – 3)
Instructional Resources (print materials, technology): On Core
Mathematics (Houghton Mifflin Harcourt,),
www.kutasoftware.com (Practice worksheets)
http://www.ms.uky.edu/algebracubed/lessons/ShadowProject.pdf,
(MG.3 and SRT.5)
http://www.regentsprep.org/Regents/math/geometry/GP11/indexGP
11.htm (C.1 AND SRT.2)
http://www.regentsprep.org/Regents/math/geometry/GT3/indexGT3
.htm (CO.2, SRT.1)
http://sdshs.net/ourpages/auto/2009/8/22/56632077/hw_21%20Chor
d%20Properties.pdf (discovery activity pages 27 – 29, SRT.3 and
C.1)
Guided Investigation 9.1 – 9.3 (patty paper foldable activity and
discovering station. SRT.1, CO.2)
Pythagorean Theorem project and how it relates to certain jobs,
Real world applications (SRT.3)
http://www.meikemcdonald.com/Pages/Geometry.aspx (random
worksheets and projects ideas all standards)
Tessellation Project – wrap up project (CO.2)
Geometry in the trees – exploratory activity for side splitter theorem
with exercises (SRT.3)
Facilitator’s Role: lecture, guided instruction, assign cooperative group
job responsibilities, monitor student progress, and facilitate learning
Assessment: Teacher made quizzes and tests (On Core Mathematics –
Examview),
http://www.regentsprep.org/Regents/math/geometry/GP11/indexGP
11.htm (Online quizzes and problems C.1 AND SRT.2)
http://www.regentsprep.org/Regents/math/geometry/GT3/indexGT3
.htm (Online quizzes and problems CO.2, SRT.1)
http://sdshs.net/ourpages/auto/2009/8/22/56632077/hw_21%20Chor
d%20Properties.pdf (discovery activity pages 27 – 29, SRT.3, C.1
black line masters.)
Notes and Additional Information: Pending initial instruction of unit
Geometry
Quadrilaterals Project – A
Name:____________________
Due Date:______________
NAME THAT FIGURE!
In this project, you will be given four coordinate points and will use the distance
formula and slope formula to find information about congruent segments, parallel
lines, and right angles. You will then use this information to name the figure drawn
by connecting the points.
Follow the instructions below and record the specified information for figure one.
Repeat the process for figure two. Neatness and creativity will affect your grade.
Figure One
A (1, 7)
B (7, 8)
C (8, 2)
D (2, 1)
1. In a coordinate plane (using graph paper), plot the points above and connect
the points in order.
2. Find the distance for each side of quadrilateral ABCD. (Use the distance
formula and show work.)
3. Find the slope for each side of quadrilateral ABCD. (Use the slope formula
and show work.)
Use the results from #2 and #3 to make any conclusions about:
4.
5.
6.
7.
8.
Parallel Lines
Congruent Sides
Consecutive Congruent Sides
Right Angles
Use the information from #1-7 to name the figure as specifically as possible.
(For example, if a figure is a square, do not name it a rectangle.)
Figure Two
A (2, 0)
B (7, 1)
C (8, 5)
D (3, 4)
Repeat the process for the coordinates for Figure Two.
Geometry
Name:_______________________
“Name that Figure” Project
Grading Rubric
Figure 1 – Components
Figure 2 - Components
Graph (1)
_____
Graph (1)
_____
Distance (1)
_____
Distance (1)
_____
Slope (1)
_____
Slope (1)
_____
Analysis (1)
_____
Analysis (1)
_____
Conclusion (1)
_____
Conclusion (1)
_____
Figure 1 – Accuracy
Figure 2 - Accuracy
Graph (1)
_____
Graph (1)
_____
Distance (1)
_____
Distance (1)
_____
Slope (1)
_____
Slope (1)
_____
Analysis (1)
_____
Analysis (1)
_____
Conclusion (2)
_____
Conclusion (2)
_____
Figure 1 Total (11)
_____
Figure 2 Total (11)
_____
Creativity (4)
_____
Neatness (4)
_____
Total (30)
_____
(-3 per day late)
_____
GRADE
_____