CCSS.Math.Content.HSG-CO.B

CCSS.Math.Content.HSG-CO.B is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSG-CO.B.6

  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...

• CCSS.Math.Content.HSG-CO.B.7

  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 correspondin...

• CCSS.Math.Content.HSG-CO.B.8

  Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

01

What Students Need to Do

Students map one figure onto another with translations, rotations, and reflections. They describe the sequence precisely and use preserved lengths and angles to justify congruence. They also connect these moves to triangle congruence tests.

02

What Mastery Looks Like

A student can choose and describe moves that carry every vertex of one figure onto its matching vertex. They can predict image coordinates and explain how SSS, SAS, or ASA establishes triangle congruence.

03

Common Misconceptions

Students may call figures congruent when one is a scaled copy. They may treat a dilation as a move that preserves congruence. They may match vertices in the wrong order or assume equal area proves congruence.

04

How to Assess It

Give triangle ABC with A(0,0), B(3,0), C(0,2) and triangle A'B'C' with A'(4,1), B'(1,1), C'(4,3). Ask students to name a sequence of moves mapping ABC onto A'B'C' and explain why the triangles are congruent.

1. 01

   Use tracing paper to slide, turn, and flip one triangle onto another, then record each move in order.

2. 02

   Ask students to explain why rotating a figure preserves side lengths and angle measures, using one labeled example.

3. 03

   Play Match the Motion with card pairs showing figures and coordinate rules, and have students justify each match.

4. 04

   Compare repeated tile patterns, then identify the translations, rotations, or reflections that carry one tile image onto another.

• CCSS.Math.Content.8.G.A.2

  Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and trans...