OBJECTIVE - G.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 definition of congruence in terms of rigid motions to decide if they are congruent.

INTERPRETATION OF OBJECTIVE - G.CO.B.6

This particular objective connects isometric transformations to congruence. So this is where isometric gets put away and we start to use congruence. This is a major difference, that congruence is being defined as a single or sequence of transformations that map one onto the other.

This is the setup for determining the congruence between any two figures.

I think the 'predict the effect' phrase refers to understanding the coordinate rules for the transformations and predicting the transformation based on the rule.

SKILLS

(1) The student will be able to show two figures are congruent if there is a sequence of rigid motions that map one figure to another.

(2) The student will be able to show that two figures are congruent if and only if they have the same shape and size.

(3) The student will be able to use composite transformations to map on figure onto another.

(4) The student will be able to recognize the effects of rigid motion on orientation and location of a figure.

(5) The student will be able to use the definition of congruence as a test to see if two figures are congruent.

THE BIG IDEA

Congruence is the mapping of one shape onto another through one or more isometric transformations. Done!

ΔBCD ≅ ΔB''C''D'' because ΔBCD is translated by vector<BB'> and then reflected onto ΔB''C''D'' .

TRAPS & PITFALLS

No real traps or pitfalls here - not if you have introduced the previous concepts correctly.

PAST CONNECTIONS

Students will use the concepts covered in G.CO.4 and G.CO.5. The definitions and the composite transformations will link isometry to congruence.

FUTURE CONNECTIONS

This is the developing of the connection to congruence. The next few objectives will rely heavily on this definition of congruence.

MY REFLECTIONS (over line l)

The truth is that by the time we get to this point, the students think that we have been doing congruence for a week or so.  When we did constructions we talked about congruent segments and angles… when we talked about isometric transformations students started calling that congruence… and so by now… it feels pretty normal.