Download Congruent Triangles

PENNSYLVANIA
Date: March 5, 2014 ET
Susquenita Curriculum
Course: .PACC Academic Geometry
Teacher / Team Name: LARA
Curriculum:
Topic:
004 Congruent Triangles
Days: 13
Subject(s): Math
Know:
1 -- Essential
Make sense of problems
and persevere in solving
them.
2 -- Essential
Reason abstractly and
quantitatively.
3 -- Essential
Construct viable
arguments and critique
the reasoning of others.
4 -- Essential
Model with
mathematics.
5 -- Essential
Use appropriate tools
strategically.
6 -- Essential
Attend to precision.
7 -- Essential
Look for and make use
of structure.
8 -- Essential
Look for and express
regularity in repeated
reasoning.
CC.2.3.HS.A.3 -Essential
Verify and apply
geometric theorems as
they relate to geometric
figures.
CC.2.3.HS.A.4 -Essential
Apply the concept of
congruence to create
geometric constructions.
Grade(s): 7th, 8th, 9th, 10th, 11th, 12th
Understand:
Congruency guarantees
that a triangle with given
conditions cannot be
distorted.
Do:
1 -- Essential
Make sense of problems and persevere in solving
them.
2 -- Essential
Reason abstractly and quantitatively.
3 -- Essential
Construct viable arguments and critique the reasoning
of others.
4 -- Essential
Model with mathematics.
5 -- Essential
Use appropriate tools strategically.
6 -- Essential
Attend to precision.
7 -- Essential
Look for and make use of structure.
8 -- Essential
Look for and express regularity in repeated reasoning.
CC.2.3.HS.A.3 -- Essential
Verify and apply geometric theorems as they relate to
geometric figures.
CC.2.3.HS.A.4 -- Essential
Apply the concept of congruence to create geometric
constructions.
CC.2.3.HS.A.14 -- Essential
Apply geometric concepts to model and solve real
world problems.
G.1.2.1.1 -- Essential
Identify and/or use properties of triangles.
Page 1 of 3
PENNSYLVANIA
Date: March 5, 2014 ET
Susquenita Curriculum
Course: .PACC Academic Geometry
Teacher / Team Name: LARA
Curriculum:
Topic:
004 Congruent Triangles
Days: 13
Subject(s): Math
Know:
CC.2.3.HS.A.14 -Essential
Apply geometric
concepts to model and
solve real world
problems.
Grade(s): 7th, 8th, 9th, 10th, 11th, 12th
Understand:
Do:
G.1.2.1.3 -- Essential
Identify and/or use properties of isosceles and
equilateral triangles.
G.1.3.1.1 -- Essential
Identify and/or use properties of congruent and similar
polygons or solids.
G.1.2.1.1 -- Essential
Identify and/or use
properties of triangles.
G.1.2.1.3 -- Essential
Identify and/or use
properties of isosceles
and equilateral triangles.
G.1.3.1.1 -- Essential
Identify and/or use
properties of congruent
and similar polygons or
solids.
Page 2 of 3
Susquenita Curriculum
Course: .PACC Academic Geometry
Teacher / Team Name: LARA
Curriculum:
Topic:
004 Congruent Triangles
Subject(s): Math
Which standards are students learning in this unit?
PENNSYLVANIA
Date: March 5, 2014 ET
Days: 13
Grade(s): 7th, 8th, 9th, 10th, 11th, 12th
1 -- Essential
Make sense of problems and persevere in solving them.
2 -- Essential
Reason abstractly and quantitatively.
3 -- Essential
Construct viable arguments and critique the reasoning of others.
4 -- Essential
Model with mathematics.
5 -- Essential
Use appropriate tools strategically.
6 -- Essential
Attend to precision.
7 -- Essential
Look for and make use of structure.
8 -- Essential
Look for and express regularity in repeated reasoning.
CC.2.3.HS.A.3 -- Essential
Verify and apply geometric theorems as they relate to geometric figures.
CC.2.3.HS.A.4 -- Essential
Apply the concept of congruence to create geometric constructions.
CC.2.3.HS.A.14 -- Essential
Apply geometric concepts to model and solve real world problems.
G.1.2.1.1 -- Essential
Identify and/or use properties of triangles.
G.1.2.1.3 -- Essential
Identify and/or use properties of isosceles and equilateral triangles.
G.1.3.1.1 -- Essential
Identify and/or use properties of congruent and similar polygons or solids.
Page 3 of 3
PENNSYLVANIA
Date: March 5, 2014 ET
Susquenita Curriculum
Course: .PACC Academic Geometry
Teacher / Team Name: LARA
Curriculum:
Topic:
004 Congruent Triangles
Days: 13
Subject(s): Math
Grade(s): 7th, 8th, 9th, 10th, 11th, 12th
Key Learning: Classifying triangles by sides and angles can assist you in proving that triangles are congruent.
Unit Essential Question(s):
How do you use triangle classifications to prove
that triangles are congruent?
Concept:
Concept:
Concept:
4.1 Triangle Sum Properties
4.2 Congruence and Triangles
CC.2.3.HS.A.14, CC.2.3.HS.A.3, G.1.2.1.1
CC.2.3.HS.A.14, CC.2.3.HS.A.3, CC.2.3.HS.A.4, G.1.2.1.1 , G.
4.4 Prove Triangles Congruent by
SSS
1.3.1.1
CC.2.3.HS.A.14, CC.2.3.HS.A.3, CC.2.3.HS.A.4, G.1.2.1.1 , G.
1.3.1.1
Lesson Essential Question(s):
1.How do you classify triangles by sides and
angles? (ET)
Lesson Essential Question(s):
Lesson Essential Question(s):
2.How do you determine if shapes are identical? 3.How do you use the sides of a triangle to
(A)
determine congruency? (A)
Vocabulary:
acute triangle, right triangle, obtuse triangle,
scalene triangle, isosceles triangle, equilateral
triangle, equiangular triangle, interior angles,
exterior angles, corollary to a theorem
Vocabulary:
congruent figures, corresponding parts
Vocabulary:
congruent figures, corresponding parts
Concept:
Concept:
Concept:
4.5 Prove Triangles Congruent by
SAS and HL
4.6 Prove Triangles Congruent by
ASA and AAS
4.7 Congruent Triangles
CC.2.3.HS.A.14, CC.2.3.HS.A.3, CC.2.3.HS.A.4, G.1.2.1.1 , G.
CC.2.3.HS.A.14, CC.2.3.HS.A.3, CC.2.3.HS.A.4, G.1.2.1.1 , G.
1.3.1.1
1.3.1.1
Lesson Essential Question(s):
4.How do you use SAS and HL to prove that
two triangles are congruent? (A)
Lesson Essential Question(s):
5.How do you use ASA and AAS to prove that
two triangles are congruent? (A)
Lesson Essential Question(s):
6.What is CPCTC and how is it used to prove
that parts of two triangles are congruent? (A)
Vocabulary:
leg of a right triangle, hypotenuse
Vocabulary:
flow proof
Vocabulary:
CC.2.3.HS.A.14, CC.2.3.HS.A.3, CC.2.3.HS.A.4, G.1.2.1.1 , G.
1.3.1.1
Page 1 of 2
PENNSYLVANIA
Date: March 5, 2014 ET
Susquenita Curriculum
Course: .PACC Academic Geometry
Teacher / Team Name: LARA
Curriculum:
Topic:
004 Congruent Triangles
Days: 13
Subject(s): Math
Grade(s): 7th, 8th, 9th, 10th, 11th, 12th
Concept:
Concept:
4.8 Isosceles and Equilateral
Triangles
4.9 Perform Congruence
Transformations
Concept:
CC.2.3.HS.A.14, CC.2.3.HS.A.3, G.1.2.1.1 , G.1.2.1.3, G.1.3.1.1 CC.2.3.HS.A.14, CC.2.3.HS.A.3, CC.2.3.HS.A.4, G.1.2.1.1 , G.
1.3.1.1
Lesson Essential Question(s):
7.How do you use the properties of isosceles
and equilateral triangles to find measures in a
triangle? (A)
Lesson Essential Question(s):
8.How do you use transformations to create
congruent figures? (A)
Lesson Essential Question(s):
Vocabulary:
legs, vertex angle, base, base angles
Vocabulary:
transformation, image, translation, reflection,
rotation, congruence transformation
Vocabulary:
Additional Information:
rulers, protractors, manipulatives
Attached Document(s):
Page 2 of 2
Susquenita Curriculum
Course: .PACC Academic Geometry
Teacher / Team Name: LARA
Curriculum:
Vocab Report for Topic:
004 Congruent Triangles
Subject(s): Math
PENNSYLVANIA
Date: March 5, 2014 ET
Days: 13
Grade(s): 7th, 8th, 9th, 10th, 11th, 12th
Concept: 4.1 Triangle Sum Properties
acute triangle right triangle obtuse triangle scalene triangle isosceles triangle equilateral triangle equiangular triangle interior angles exterior angles corollary to a theorem
-
Concept: 4.2 Congruence and Triangles
congruent figures corresponding parts
-
Concept: 4.4 Prove Triangles Congruent by SSS
congruent figures corresponding parts
-
Concept: 4.5 Prove Triangles Congruent by SAS and HL
leg of a right triangle hypotenuse -
Concept: 4.6 Prove Triangles Congruent by ASA and AAS
flow proof
-
Concept: 4.8 Isosceles and Equilateral Triangles
legs vertex angle base base angles
-
Concept: 4.9 Perform Congruence Transformations
Page 1 of 2
Susquenita Curriculum
Course: .PACC Academic Geometry
Teacher / Team Name: LARA
Curriculum:
Vocab Report for Topic:
004 Congruent Triangles
Subject(s): Math
PENNSYLVANIA
Date: March 5, 2014 ET
Days: 13
Grade(s): 7th, 8th, 9th, 10th, 11th, 12th
transformation image translation reflection rotation congruence transformation
-
Page 2 of 2