Math Scale

Information for the Teacher

Subject:
Geometry / Domain:
Geometry / Topic:
Triangle Congruence
Cluster Statement:
Understanding congruence in terms of rigid motions
Standard(s):
G.CO.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 corresponding pairs of angles are congruent. / DOK:
3
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. / 3
Potential Mathematical Practice Standard(s):
MP2 Reason abstractly and quantitatively.
MP3 Construct viable arguments and critique the reasoning of others.
Notes:
AAS is not specifically referenced in the standard or scale because it is a special case of ASA (once you know two angles you automatically know the third). If it is taught you may add it to the scale appropriately.
Students should be asked to investigate multiple triangles with the given parameters of SSS, SAS, and ASA, and how they are all the same, if the parameters are the same. For examples, if you give the entire class the same two sides, the same included angle, can any student create a resulting triangles that is different from others?

Mathematics

Topic: Triangle Congruence in terms of rigid motion
Scale
Score
4.0 / I can write a coordinate proof to prove that two shapes are congruent in terms of rigid motions.
I can analyze why the criteria of AAA and SSA does not represent triangle congruence.
/ I can explain the relationship between rigid transformations and ASA, SAS, and SSS that produce congruent triangles.
I can use rigid transformation to compare triangles and apply ASA, SAS, and SSS to formulate congruence statements, when appropriate.
I can show that two triangles are congruent if and only if the corresponding parts are congruent using the definition of congruence in terms of rigid motions.
Score
2.0 / I can identify a sequence of rigid motions that map a triangle onto its congruent image.
Score
1.0 / I can identify when two figures are congruent by using rigid transformation.
I can define rigid motion in terms of preserving side length and angle measure.
Score
0.0 / I cannot yet define rigid motion.

Triangle Congruence (G.CO.7-8) www.tbaisd.org 11.24.2015