4-3 Congruent Triangles Congruent triangles Triangles that are the same size and shape All of the vertices correspond/ “match up” The sides of the triangles also correspond All the parts that match are called corresponding parts. Angles A  F B  D C  E Segments AB  FD BC  DE AC  FE If two triangles are congruent, the vertices correspond in the same order as the letters naming the triangles. A B C F D E ABC  FDE

Definition of Congruent Triangles If the corresponding parts of two triangles are congruent, then the two triangles are congruent. If two triangles are congruent, then the corresponding parts of the two triangles are congruent. Abbreviation: CPCTC Corresponding Parts of Congruent Triangles are

Example #1 If BIG  CAT, name the congruent angles and sides. Then draw the triangles, using the arcs and slash marks to show congruent angles and sides. Label your first triangle with the first set of letters. Starting in the same spot on the other triangle, name it using the second set of letters. Then figure out the corresponding parts. Then draw your markings. Angles B  C I  A G  T Segments BI  CA IG  AT BG  CT I A T B G C

Check Your Progress 1A & 1B The measures of the sides of triangles PDQ and OEC are PD = 5, DQ = 7, PQ = 11, EC = 7, OC = 5, and OE = 11 1A: Name the corresponding congruent angles and sides 1B: Name the congruent triangles

Theorem 4.4 Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric, and transitive

Example #2 Write down one triangle. HAT Figure out what angle corresponds to the order you used. H  B A  O T  Y So HAT  BOY The corresponding parts of two congruent triangles are marked on the figure. Write a congruence statement for the two triangles. A congruence statement says ???  !!! A B Y H T O

Transformations Congruence Transformations: The shapes maintain their congruence throughout each transformation. Rotation (turn) Reflection (flip) Transition (slide)

Take a look at Example #2 p. 219 Now do Check your Progress 2A & 2B p. 220 Answers 2A: LM = MN = LN = 4, L’M’ = M’N’ = L’N’ = 4