Download Bundle 2 Geometry - East Allen County Schools

EAST ALLEN COUNTY SCHOOLS
Bundle 2
Geometry
Congruence in
Proofs
Big Idea: Deductive Reasoning
Enduring Understandings
Essential Questions
Relationships between angles and sides can be used to prove the congruence of
triangles.
Properties of parallelograms and triangles have useful real-world applications.
Congruent geometric figures are modeled through constructions using a specific
sequence of steps and processes.
CC/Learning Targets
G.CO.7
G.CO.8
G.CO.9
G.CO.10
G.CO.11
G.CO.12
G.CO.13
What rotation, reflection and/or translation transforms figures while maintaining
congruence?
What relationships do angles and sides have in proving triangle congruence?
What is special about angles formed by two or more lines?
What are the properties of special parallelograms?
What are the properties of special triangles?
How would you use constructions and the coordinate plane to represent
geometric figures?
Core Vocabulary
Links to Technology
alternate interior/exterior angles
biconditional statement
conditional statement
corresponding angles
negation
theorem
transversal
Bundle Performance Task(s)
Students will create a board game (monopoly, clue, chutes and ladders, life) that will have questions pertaining to the following topics:
Statement/justifications of proof
Properties of parallelograms
Properties of special triangles
Properties of special angle pairs
Congruence of triangles
Misc.
The game is to last a minimum of 15 – 30 minutes. All supplies needed to play the game are to be included.
A list of questions with answers is to be submitted with the game.
A possible assessment rubric is provided in the Appendix under Curriculum for each Performance Task.
Geometry
Bundle 2
Quarter 1
Sept.-Oct.
Geometry
CC/Learning Targets
G.CO.7
(G.4.3a)
G.CO.8
(G.4.6c)
G.CO.9
(G1.2f)
(G.1.3a-d)
(G.8.8a)
G.CO.10
(G.4.1a-b)
(G.4.2a-b)
(G.4.9a-b)
(G.8.8a)
Use the definition of congruence in
terms of rigid motions to show that two
triangles are congruent if and only if
corresponding pairs of sides and
corresponding pairs of angles are
congruent.
Explain how the criteria for triangle
congruence (ASA, SAS, and SSS)
follow from the definition of
congruence in terms of rigid motions.
Prove theorems about lines and
angles. Theorems include: vertical
angles are congruent; when a
transversal crosses parallel lines,
alternate interior angles are congruent
and corresponding angles are
congruent; points on a perpendicular
bisector of a line segment are exactly
those equidistant from the segment’s
endpoints.
Prove theorems about triangles.
Theorems include: measures of
interior angles of a triangle sum to
180°; base angles of isosceles
triangles are congruent; the segment
joining midpoints of two sides of a
triangle is parallel to the third side and
half the length; the medians of a
Bundle 2
Resource of Ideas
-AAS Congruence
-HL
-ASA
-SSA not enough information
-SSS
-SAS
-Prentice Hall Mathematics
Lessons 3.7, 4.2, 4.3, 4.6
-Triangle congruence
-Prentice Hall Mathematics
Lessons 4.2, 4.3, 4.6, 4.7
-Special angles when lines are parallel
-Prentice Hall Mathematics
Lessons 3.1, 3.2, 5.5
-iBook Prentice Hall Geometry
Lessons 2.1-2.6, 3.1-3.3,5.2
-Proof of sum of angles in triangle is 180
-Isosceles triangles
-Isosceles triangle proof-Kahn Academy
-Midsegment of a triangle properties and uses
-Special segment in triangle median
-Point of concurrency median
Evidence of Learning
-Homework
-White Boards
-Entrance/Exit tickets
-Nearpod
-Journal
-Homework
-Quiz/Test
-Worksheet
-Journal
-Proof
-Patty Paper
-Flash Card/Note Card
-Quiz
-Journal
-Proof
-Paddy Paper
-Constructions
-Homework
-Journal
Geometry
G.CO.11
(G.2.3a)
(G.3.1a)
(G.3.1c-f)
(G.3.4a-b)
(G.8.8a)
G.CO.12
(G.1.2b-e)
(G.1.2g)
(G.2.4d-e)
(G.4.2c-f)
(G.4.2h,I, k)
(G.8.9a-c)
G.CO.13
(G4.2d, j)
(G.6.4a-b)
(G7.6c)
(G.8.9a)
Bundle 2
triangle meet at a point.
-Prentice Hall Mathematics
Lessons 3.3, 5.3
-iBook Prentice Hall Geometry
Lessons 2.1-2.5, 3.5, 4.5, 5.1, 5.4-5.7
Prove theorems about parallelograms.
Theorems include: opposite sides are
congruent, opposite angles are
congruent, the diagonals of a
parallelogram bisect each other, and
conversely, rectangles are
parallelograms with congruent
diagonals.
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.
Construct an equilateral triangle, a
square, and a regular hexagon
inscribed in a circle.
-Practice parallelogram proofs
Correlating CC/Learning Targets
-Entrance/Exit Ticket
-Nearpod
-White boards
-Patty Paper
-Flash Card/Note Card
-Journal
-Prentice Hall Mathematics
Lessons 4.1, 4.4, 6.1, 6.2, 6.4, 6.6, 6.7, 8.6
-iBook Prentice Hall Geometry
Lessons 2.1-2.5, 6.2-6.5
-Constructing a segment
-Angle bisector
-Constructions
-Journal
-Small Group Discussion
-Quiz/Test
-Prentice Hall Mathematics
Lessons 1.5, 5.2, 5.3
-iBook Prentice Hall Geometry
Lessons 1.6, 3.2, 3.6, 4,4
-Construction an equilateral triangle
-Regular polygons inscribed in a circle
-Construction
-Journal
-Quiz/Test
-Patty Paper
-Prentice Hall Mathematics
Lessons 1.5, 5.3, 11.1
-iBook Prentice Hall Geometry
Lessons 3.6, 4.5, 5.1, 10.3
Teacher Notes
Geometry
G.CO.1
G.CO.2
G.CO.3
G.CO.4
G.CO.5
G.CO.6
Bundle 2
G.GPE.5
G.GPE.6
All embedded apps included in this curriculum are free.
iTunes U, Northest Arkasas Education Cooperative Geometry
Lesson 6 Polygon Identification