Download Focus Topic 6 – Congruent Triangles

Geometry Curriculum Map
2013-2014
Focus Topic 6 – Congruent Triangles
(3 Weeks)
G.SRT.B.5 – Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures.
Learning Target(s):
 I can recall congruence and similarity criteria for triangles.
 I can use congruency and similarity theorems for triangles to solve problems.
 I can use congruency and similarity theorems for triangles to prove relationships in geometric figures.
G.CO.B.6 (Supporting Standard) – Use geometric descriptions of rigid motions to transform figures and
to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent.
Learning Target(s):
 I can use geometric descriptions of rigid motions to transform figures.
 I can predict the effect of a given rigid motion on a given figure.
 I can, given two figures, use the definition of congruence in terms of rigid motions to decide if they
are congruent.
G.CO.B.7 (Supporting Standard) – 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.
Learning Target(s):
 I can identify corresponding angles and sides of two triangles.
 I can identify corresponding pairs of angles and sides of congruent triangles after rigid motions.
 I can use the definition of congruence in terms of rigid motions to show that two triangles are
congruent if corresponding pairs of sides and corresponding pairs of angles are congruent.
 I can use the definition of congruence in terms of rigid motions to show that if the corresponding
pairs of sides and corresponding pairs of angles of two triangles are congruent then the two triangles
are congruent.
 I can justify congruency of two triangles using transformations.
G.CO.B.8 (Supporting Standard) – Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow from the definition of congruence in terms of rigid motions.
Learning Target(s):
 I can informally use rigid motions to take angles to angles and segments to segments.
 I can formally use dynamic geometry software or straightedge and compass to take angles to angles
and segments to segments.
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Curriculum and Instruction
2013-14
Geometry Curriculum Map
2013-2014

I can explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of
congruence in terms of rigid motions.
Vocabulary: ASA, congruent, congruence, corresponding, criteria, rigid motions, SAS, similar, similarity,
SSS
Instructional Notes:
 Instruction should focus on congruence criteria during this Focus Topic. Similarity criteria are
addressed in Focus Topic 4. (G.SRT.B.5)
 Instruction should emphasize rigid motions as the foundation of the definition of congruence.
(G.CO.B.6, G.CO.B.7, G.CO.B.8)
 Instruction should allow students to reason from the basic properties of rigid motions (that they
preserve distance and angle), which are assumed without proof. (G.CO.B.6, G.CO.B.7, G.CO.B.8)
 Instruction should emphasize that rigid motions and their assumed properties can be used to
establish the usual triangle congruence criteria, which can then be used to prove other theorems.
(G.CO.B.6, G.CO.B.7, G.CO.B.8)
 Supporting standards do not have to be directly incorporated into instruction for all students, but for
students that have mastered the focus and foundational standards, supporting standards should be
incorporated.
 For students in Advanced or Honors courses, supporting standards are to be incorporated into
instruction within the time frame allowed for the Focus Topic.
Instructional Resources:
 Formative Assessment Lessons for Mathematics: http://map.mathshell.org/materials/lessons.php
 Formative Assessment Tasks for Mathematics: http://map.mathshell.org/materials/tasks.php
 Illustrative Mathematics: http://www.illustrativemathematics.org/standards/k8
 NCTM Illuminations: http://illuminations.nctm.org/
 PARCC: http://www.parcconline.org/mcf/mathematics/parcc-model-content-frameworks-browser
 Inside Mathematics: http://insidemathematics.org/index.php/mathematical-content-standards
 New York State: http://www.engageny.org/mathematics
 Lessons from Geometry Connections: 6.1.1 – 6.1.3, 7.2.6, 8.2.1, 8.2.4 (G.SRT.B.5)
 Lessons from Geometry Connections: 2.1.1 – 2.1.2 (G.CO.B.6)
 Lessons from Geometry Connections: 6.1.2 (G.CO.B.7)
 Lessons from Geometry Connections: 7.1.3, 7.2.1 – 7.2.2 (G.CO.B.8)
Assessment Notes:
 The Focus Topic will have 3 multiple choice questions and 1 extended response on the proficiency
assessment.
 Supporting standards will not be directly assessed on proficiency assessments.
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Curriculum and Instruction
2013-14