Download Unit 2-Triangle_Properties_Congruence

Unit Map 2012-2013
City School District of Albany
Collaboration / Geometry District Curriculum September 2012* (C) / Grade 10
(District High School Curriculum)
Tuesday, January 15, 2013, 9:54AM
Unit: Triangle Properties & Congruence (Week 8, 8 Weeks)
Priority Standards
Math (2005), HS: Geometry, Geometry
Locus

G.G.21 Investigate and apply the concurrence of medians, altitudes, angle bisectors, and
perpendicular bisectors of triangles
Students will identify and justify geometric relationships formally and informally.
Informal and Formal Proofs









G.G.27 Write a proof arguing from a given hypothesis to a given conclusion
G.G.28 Determine the congruence of two triangles by using one of the five congruence techniques
(SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two
congruent triangles
G.G.29 Identify corresponding parts of congruent triangles
G.G.36 Investigate, justify, and apply theorems about the sum of the measures of the interior and
exterior angles of polygons
G.G.37 Investigate, justify, and apply theorems about each interior and exterior angle measure of
regular polygons
G.G.38 Investigate, justify, and apply theorems about parallelograms involving their angles, sides,
and diagonals
G.G.42 Investigate, justify, and apply theorems about geometric relationships, based on the
properties of the line segment joining the midpoints of two sides of the triangle
G.G.43 Investigate, justify, and apply theorems about the centroid of a triangle, dividing each
median into segments whose lengths are in the ratio 2:1
G.G.48 Investigate, justify, and apply the Pythagorean theorem and its converse
Supporting Standards
SUPPORTING: CCLS:Mathematics, HS: Geometry, Congruence
G-CO Understand congruence in terms of rigid motions

8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow from the definition of congruence in terms of rigid motions.
G-CO Prove geometric theorems

9. Prove theorems about lines and angles.

10. Prove theorems about triangles.
SUPPORTING: CCLS:Mathematics, HS: Geometry, Similarity, Right Triangles, & Trigonometry
G-SRT Define trigonometric ratios and solve problems involving right triangles

6. Understand that by similarity, side ratios in right triangles are properties of the angles in
the triangle, leading to definitions of trigonometric ratios for acute angles.

8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
SUPPORTING: CCLS:Mathematics, HS: Geometry, Circles
G-C Understand and apply theorems about circles

3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.
"Unwrapped" Content


concurrence of
medians, altitudes,
angle bisectors, and
perpendicular
bisectors of triangles
theorems about:




the sum of the
measures of
the interior
and exterior
angles of
polygons
each interior
and exterior
angle measure
of regular
polygons
parallelograms
involving their
angles, sides,
and diagonals
geometric
relationships,
based on the
properties of
the line
segment
joining the
midpoints of
two sides of
the triangle


the centroid of
a triangle,
dividing each
median into
"Unwrapped" Skills





INVESTIGATE and APPLY the
concurrence of medians, altitudes, angle
bisectors, and perpendicular bisectors of
triangles
INVESTIGATE, JUSTIFY and APPLY
theorems about angles, diagonals and
sides
WRITE a proof arguing from a given
hypothesis to a given conclusion
IDENTIFY corresponding parts
DETERMINE the congruence of triangles
Bloom's Taxonomy
Levels
2, 4 (know and apply points
of concurrency)
2, 4, 6 (investigate, apply
and justify)
3 (write)
1 (identify)
3 (determine)

segments
whose lengths
are in the
ratio 2:1
the
Pythagorean
theorem and
its converse

proof arguing from a
given hypothesis to a
given conclusion

corresponding parts
of congruent
triangles

congruence of two
triangles by using
one of the five
congruence
techniques (SSS,
SAS, ASA, AAS, HL),
given sufficient
information about the
sides and/or angles
of two congruent
triangles
Big Ideas
Essential Questions
concept of proof
How is it possible to prove that two figures are congruent or
not congruent?
concept of corresponding parts
Does order matter when comparing figures?
definitions of medians, altitudes, bisectors, What relationships remain the same and which change when
constructing medians and bisectors?
diagonals, midpoints
congruence vs similar
What is the difference between congruent shapes and similar
shapes?
Themes
Vocabulary Terms & Concepts
congruence
corresponding parts
similarity
bisectors
medians
perpendicular
proof
diagonals
exterior angles
interior angles
parallelogram
centroid
incenter
circumcenter
Standardized Assessment Informal Progress Monitoring Checks
Correlations
Pre-Assessment
Unit 2 post test
Unit 2 pre test
Unit 2 post test
Post-Assessments
Unit1post_b.tst
Engaging Learning Experiences
Research-Based Effective Teaching
Strategies




Identifying Similarities and
Differences
Summarizing and Note Taking
Reinforcing Effort, Providing
Recognition
Homework and Practice
21st Century Learning Skills



Critical thinking and Problem Solving
Effective Oral and Written Communication
Accessing and Analyzing Information




Cooperative Learning
Setting Objectives, Providing
Feedback
Generating and Testing
Hypotheses
Differentiation Strategies Specifically Designed Instruction for SPED
Student
Intervention Strategies
(Tier 1, 2, 3)
proofs_levels[2].docx
Strategies for English
Language Learners
Enrichment/Extension
Pythagorean theorem and corollary
if a^2 + b^2 > c^2 then then triangle is acute
if a^2 + b^2 = c^2 then then triangle is right
if a^2 + b^2 < c^2 then then triangle is obtuse
Always remember that the third side must be
between the sum and the difference of the
measures of the other two sides
Instructional Resources
Unit 2 post review
Unit 2 post test
Triangles notebook
Chapter 4 review
Chapter 4 test
Chapter 5 review
Chapter 5 test
Triangles proof notebook will not upload....maybe to large?
Triangles proof quiz
Exit tickets
Interdisciplinary
Connections
Unit2_post_review.tst
Unit2_posttestt_v2.tst
Chapter 4 Review.tst
Chapter 4 test.tst
proofs_levels.docx
Exit ticket midsegment.docx
Triangles.2012.2013.notebook
Chapter 5 REVIEW.tst
Quiz1 2012-2013.docx
congruent.triangles.2012.2013.notebook
Last Updated: Monday, January 7, 2013, 8:47PM
Atlas Version 7.2.6
© Rubicon International 2013. All rights reserved