Download Export To Word

Standard #: MAFS.912.G-CO.2.7
This document was generated on CPALMS - www.cpalms.org
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.
Subject Area: Mathematics
Grade: 912
Domain: Geometry: Congruence
Cluster: Understand congruence in terms of rigid motions - Geometry - Major Cluster
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so
would strip the coherence of the mathematical ideas and miss the opportunity to enhance the
major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved
Related Courses
Course Number
1206300:
7912060:
1206315:
1206310:
1206320:
Course Title
Informal Geometry (Specifically in versions: 2014 - 2015, 2015
and beyond (current))
Access Informal Geometry (Specifically in versions: 2014 2015 (course terminated))
Geometry for Credit Recovery (Specifically in versions: 2014 2015, 2015 and beyond (current))
Geometry (Specifically in versions: 2014 - 2015, 2015 and
beyond (current))
Geometry Honors (Specifically in versions: 2014 - 2015, 2015
and beyond (current))
7912065:
1200400:
Access Geometry (Specifically in versions: 2015 and beyond
(current))
Intensive Mathematics (Specifically in versions: 2014 - 2015,
2015 and beyond (current))
Related Access Points
Access Point
Access Point Number
MAFS.912.G-CO.2.AP.7a
Access Point Title
Use definitions to demonstrate congruency and similarity in
figures.
Related Resources
Lesson Plan
Name
Description
This lesson is intended to help you assess how well students are
able to:

Analyzing Congruence Proofs


Work with concepts of congruency and similarity,
including identifying corresponding sides and
corresponding angles within and between triangles.
Identify and understand the significance of a counterexample.
Prove, and evaluate proofs in a geometric context.
This is an exploratory lesson that elicits the relationship
Exploring Congruence Using
between the corresponding sides and corresponding angles of
Transformations
two congruent triangles.
Students will prove that two figures are congruent based on a
rigid motion(s) and then identify the corresponding parts using
Match That!
paragraph proof and vice versa, prove that two figures are
congruent based on corresponding parts and then identify which
rigid motion(s) map the images.
Slip, Slide, Tip, and Turn:
Using the definition of congruence in terms of rigid motion,
Corresponding Angles and
students will show that two triangles are congruent.
Corresponding Sides
Formative Assessment
Name
Description
Students are given two congruent triangles and asked to
Congruence Implies
determine the corresponding side lengths and angle measures
Congruent Corresponding
and to use the definition of congruence in terms of rigid motion
Parts
to justify their reasoning.
Proving Congruence Using
Students are asked to prove two triangles congruent given that
Corresponding Parts
all pairs of corresponding sides and angles are congruent.
Students are given two triangles in which all pairs of
Showing Congruence Using corresponding parts are congruent and are asked to use the
Corresponding Parts - 1
definition of congruence in terms of rigid motion to show the
triangles are congruent.
Students are given two triangles in which all pairs of
Showing Congruence Using corresponding parts are congruent and are asked to use the
Corresponding Parts - 2
definition of congruence in terms of rigid motion to show the
triangles are congruent.
Students are asked to use the definition of congruence in terms
Showing Triangles Congruent
of rigid motion to show that two triangles are congruent in the
Using Rigid Motion
coordinate plane.
Virtual Manipulative
Name
Congruent Triangles
Description
This manipulative is a virtual realization of the kind of physical
experience that might be available to students given three pieces
of straws and told to make them into a triangle. when working
with pieces that determine unique triangles (SSS, SAS, ASA).
Students construct triangles with the parts provided. After
building a red and a blue triangle, students can experience
congruence by actually moving one on the top of the other.
Problem-Solving Task
Name
Reflections and Equilateral
Triangles II
Description
This task gives students a chance to see the impact of reflections
on an explicit object and to see that the reflections do not
always commute.
Assessment
Name
Sample 1 - High School
Geometry State Interim
Assessment
Description
This is a State Interim Assessment for 9th-12th grade.
Sample 2 - High School
Geometry State Interim
Assessment
Sample 3 - High School
Geometry State Interim
Assessment
Sample 4 - High School
Geometry State Interim
Assessment
This is a State Interim Assessment for 9th-12th grade.
This is a State Interim Assessment for 9th-12th grade.
This is a State Interim Assessment for 9th-12th grades.
Student Resources
Name
Congruent Triangles
Reflections and
Equilateral Triangles
II
Description
This manipulative is a virtual realization of the kind of physical
experience that might be available to students given three pieces of
straws and told to make them into a triangle. when working with pieces
that determine unique triangles (SSS, SAS, ASA). Students construct
triangles with the parts provided. After building a red and a blue
triangle, students can experience congruence by actually moving one on
the top of the other.
This task gives students a chance to see the impact of reflections on an
explicit object and to see that the reflections do not always commute.
Parent Resources
Name
Congruent Triangles
Reflections and
Equilateral Triangles
II
Description
This manipulative is a virtual realization of the kind of physical
experience that might be available to students given three pieces of
straws and told to make them into a triangle. when working with pieces
that determine unique triangles (SSS, SAS, ASA). Students construct
triangles with the parts provided. After building a red and a blue
triangle, students can experience congruence by actually moving one on
the top of the other.
This task gives students a chance to see the impact of reflections on an
explicit object and to see that the reflections do not always commute.