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OBJECTIVE - G.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 corresponding pairs of angles are congruent.

INTERPRETATION OF OBJECTIVE - G.CO.B.7

Notice that this objective is now ONLY referring to the congruence of triangles. We are about to study triangles and their properties. This objective is establishing that if two triangles are congruent then they can be mapped onto each other using a sequence of isometric transformations and that their corresponding angles and sides are congruent.

SKILLS

(1) The student will be able to identify corresponding angles and sides based on congruence statements.

(2) The student will be able to develop and write congruence statements for two congruent triangles.

(3) The student will be able to determine if two triangles are congruent based on their corresponding parts.

THE BIG IDEA

Congruence - Most all new relationships proven or established from this point forward come from establishing triangles are congruent and that congruent triangles have many congruent parts and pieces.

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)

This seems to come quite easily. I think this is one of the reasons why we introduce congruence this way. It makes sense that if one is identical to the other (or can be mapped onto the other) that they would have to be congruent. In many ways this was a quick objective because it was an easy stepping stone to bigger ideas.