Congruent Triangles

Congruent Triangles Geometry (Holt 4-4) K. Santos

Congruent Geometric Figures Congruent Geometric Figures * have the same size and shape

Congruent Figures/Triangles (Definition) Congruent Figures----have congruent corresponding sides and congruent corresponding angles A corresponds with S ABRS B corresponds with R C corresponds with U DCUT D corresponds with T <A corresponds with <S corresponds with <B corresponds with <R corresponds with <C corresponds with <U corresponds with <D corresponds with <T corresponds with all the corrresponding parts are congruent---so ABCDSRUT

Congruent Corresponding Parts The statement: ABCDEF tells you a lot of information. It tells you about corresponding congruent angles…. < A < D < B < E < C < F It tells you about corresponding congruent sides…

Example—Corresponding parts Given: STW. Identify all pairs of congruent corresponding parts. <P <S <Q <T <R <W

Example—Finding a missing side 8 Given: . B D F 53 2x – 2 6 10 A C E Find x. AB = DE 2x - 2 = 6 2x = 8 x = 4 Find m<F. m<F = m<C Find m<C first 53 + 90 = 143 180 – 143 = 57 So m< F = 57

Example—Finding missing angles Given: . A 50 2x - 16 C B D Find x. 2x – 16 = 90 2x = 106 x = 53 Find m < D m<D = m<A m<A = 50 So m<D = 50 Find m<DBC. 90+ 50 =140 180-140=40 m<FBC = 40

Proving two triangles congruent (using definition) Given: N is a midpoint of < C < D are right triangles Prove: G C N D

Proof StatementsReasons 1. 1. Given 2. N is a midpoint of 2. Given 3. 3. definition of a midpoint 4. 4. Reflexive Property 5. < C < D 5. Given 6. 6. Given are right triangles 7. <GNC and <GND 7. definition of a right are right angles triangle 8. <GNC < GND 8. all right angles are congruent (Right angles congruent Theorem) 9. <CGN < DGN 9. Third angles theorem 10. 10. Definition of congruent triangles

Congruent Triangles