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Triangle & Geometric Congruence

Triangle & Geometric Congruence. Mr. Robinson Geometry Fall 2011. Essential Question:. How do you identify corresponding parts of congruent triangles?. The order of the ________ indicates the corresponding parts!. Δ ABC  Δ XYZ. Corresponding Parts.

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Triangle & Geometric Congruence

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  1. Triangle & Geometric Congruence Mr. Robinson Geometry Fall 2011

  2. Essential Question: How do you identify corresponding parts of congruent triangles?

  3. The order of the ________ indicates the corresponding parts! ΔABC ΔXYZ Corresponding Parts If two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles and corresponding sides are congruent. The parts of congruent triangles that “match” are called__________________. corresponding parts vertices

  4. Congruent Triangles FE DE FD AC  BC  AB  F E D In the figure, ΔABC  ΔFDE. A vertices As in a mapping, the order of the _______ indicates the corresponding parts. C B Congruent Sides Congruent Angles A  F B  D C  E These relationships help define the congruent triangles.

  5. Congruent Triangles corresponding parts If the _________________ of two triangles are congruent, then the two triangles are congruent. congruent If two triangles are _________, then the corresponding parts of the two triangles are congruent.

  6. Writing a Congruence Statement D C A B F E

  7. Congruent Triangles S Z 50° 40° R (2n + 10)° 90° Y X T ΔRST ΔXYZ. Find the value of n. ΔRST ΔXYZ identify the corresponding parts corresponding parts are congruent S  Y subtract 10 from both sides 50= 2n + 10 40= 2n divide both sides by 2 20= n

  8. 3rd Angles Theorem • If two ’s of one triangle are  to two ’s of another triangle, then the third ’s are also .

  9. ARE THESE 2 TRIANGLES CONGRUENT?

  10. Example: find x ) ) 22o )) 87o )) (4x+15)o

  11. Example: Continued 22+87+4x+15=180 4x+15=71 4x=56 x=14

  12. Properties of Congruent Triangles(Theorem 4.4) 1. Reflexive: 2. Symmetric: 3.Transitive:

  13. Congruence and Correspondence • When 2 figures are congruent there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

  14. Ex: ABCD is  to HGFE.Find x and y. F E 9cm B A (5y-12)o 91o 86o H G 113o 4x-3cm D C 4x-3=9 5y-12=113 4x=12 5y=125 x=3 y=25

  15. Assignment • P 206 – 209: 10 – 22, 22 – 29,

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