12.1 Congruence Through Constructions
Def. Similar Objects—objects that have the same shape, but not necessarily the same size. (~)
Def. Congruent Objects—objects that have the same shape and the same size. ()
Congruence Similarity, but
any circle is similar to any other circle
a circle is congruent to another circle iff .
Semicircle—when major arc = minor arc (each is semi)
construction of a line segment (Figure 10-5)
Def. Triangle—triangle (∆) ABC is congruent to ∆ A’B’C’ if A is congruent to A’, B is congruent to B’, C is congruent to C’, is congruent to , is congruent to , and is congruent to .
Construction of congruent ∆’s by SSS (Figure 10-11)
Construction of congruent angles (Figure 10-12)
Theorems 10.1 and 10.2
Construction of a bisector of a line segment