Download Mathematics Geometry Standard MAFS.912.G

Mathematics
Geometry
StandardMAFS.912.G-CO.2.8
Standard(s): MAFS.912.G-CO.2.8:
Explain how the criteria for triangle congruence (ASA, SAS,
SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.
Also assesses: MAFS.912.G-CO.2.6 and MAFS.912.G-CO.2.7
Cognitive Complexity: Level 2: Basic Application of Skills & Concepts
Assessment Limits:
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Items may require the student to justify congruence using the properties of rigid motion.
In items in which the line of reflection is given, any form of the line may be used. If the line is not a vertical
line or a horizontal line, then the line of reflection should be graphed as a dotted line.
Items should not require the student to use the distance formula.
Items may require the student to be familiar with using an algebraic description (𝒙,𝒚)→(𝒙+𝒂,𝒚+𝒃) for a
translation, and (𝒙,𝒚)→(𝒌𝒙,𝒌𝒚) for a dilation when given the center of dilation.
Items may require the student to be familiar with the algebraic description for a 90° rotation about the origin,
(𝒙,𝒚)→(−𝒚,𝒙), for a 180° rotation about the origin, (𝒙,𝒚)→(−𝒙,−𝒚), and for a 270° rotation about the origin,
(𝒙,𝒚)→(𝒚,−𝒙).
Items that use more than one transformation may ask the student to write a series of algebraic descriptions.
Items should not use matrices to describe transformations.
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The student will be able to:
• Justifies steps of a proof given algebraic descriptions of triangles, using the definition of congruence
in terms of rigid motions that the triangles are congruent using ASA, SAS, SSS, or HL.
• Uses algebraic descriptions to describe rigid motion that will prove ASA, SAS, SSS, or HL is true for
two triangles.
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The student will be able to:
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Explain how the definition of congruence in terms of rigid motions leads to triangle congruence.
Explain the triangle congruence of: ASA (Angle-Side-Angle), SAS (Side-Angle-Side), SSS (SideSide-Side) and Hypotenuse-Leg.
Applies congruence to solve problems.
Uses rigid motions to prove ASA, SAS, SSS, or HL is true for two triangles.
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The student will be able to:
• Identify corresponding parts of two congruent triangles.
• Identify the measures of the angles and/or sides of two triangles.
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The student will be able to recognize the meaning of:
• Criteria, congruence, triangle congruence, ASA – angle-side-angle, SAS – side-angle-side, SSS –
side-side-side, HL – hypontenuse-leg, rigid motions.
The student will be able to:
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Identify angles and sides in triangles.
Identify the hypotenuse and the leg in a right triangle.
Lastupdated8/11/16