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