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

 

            Similarity  Congruence

 

CONGRUENT SEGMENTS AND ANGLES

 

 

 

 

CIRCLES

 

 circle construction

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 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)

                                               

                                                Major arc

 

                                                Minor arc

 

 

 construction of a line segment (Figure 10-5)

 

 

 

 

 

 

 

 

 

 

 

 

 

TRIANGLE CONGRUENCE

 

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)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TRIANGLE PROPERTES

 

Theorems 10.1 and 10.2

 

 

 Construction of a  bisector of a line segment