CONCEPT 1 - Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure.
Rigid motions in the plane preserve the shape and size of the pre-image and image. These motions are also known as isometric transformations. It is no surprise that these two synonymous relationships lead us to congruence. In all ways, rigid motions, isometric transformations and congruence speak to the same concept – The Process of Being Identical.
|TEACHER NOTE -- This new definition of congruence is at the heart of the common core foundation. We have built all of this transformational approach for this moment in time. I think students will get this because it is so intuitive!!
Congruence of figures is defined by:
Two figures are congruent if and only if
one can be mapped onto the other by one or more rigid motions.
Translations, reflections and rotation are rigid motions and any sequence
of these from one figure onto another would prove congruence.
Dilations and other transformations that change the shape or size of the figure do not produce congruence.
A congruence statement relates one identical object to another by identifying the corresponding parts that match each other.
If these were named differently, for example Quad ABCD ≅ Quad NPMO, then their corresponding congruent parts would be different. The order that they are placed in directly relates the corresponding part.
CPCFC – Corresponding Parts of Congruent Figures are Congruent.
|Is it possible to be congruent
if SIDES ARE CONGRUENT,
BUT ANGLES ARE NOT?
Is it possible to be congruent
if ANGLES ARE CONGRUENT,
BUT SIDES ARE NOT?
Determine congruence using a single or sequence of isometric transformations.
CONCEPT 2 - Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.