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Bellwork

No Clickers. Bellwork. Problem # 49 in the Section 4.1 Homework. Bellwork Solution. Problem #49 The angles of a triangle are given as Find an equation that relates the three What are the measures of each angle. Triangle Congruency. Section 4.2. The Concept.

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Bellwork

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  1. No Clickers Bellwork • Problem #49 in the Section 4.1 Homework

  2. Bellwork Solution • Problem #49 • The angles of a triangle are given as • Find an equation that relates the three • What are the measures of each angle

  3. Triangle Congruency Section 4.2

  4. The Concept • Today we’re going to talk about how we can utilize the concept congruence in regards to triangles • You will see that the concepts are not markedly different than those discussed with angles, but instead provide additional pathways to solve triangles

  5. Defining Congruence Congruence means that the items have equal measures For triangles congruence adds a dimensions Congruent Triangles have the same measure of corresponding parts For example B O A M C N Axis of symmetry Vertex

  6. Writing Congruence The process of writing congruence statements is relatively straightforward It relies on the process of matching congruent sides and angles e.g. Write a congruency statement for the following figure A H C J K B Axis of symmetry Vertex

  7. Writing Congruence What kind of information can we get from the following statement? Axis of symmetry Vertex

  8. Using Congruence This can also be used to find angle measures For example, find x & y O 25 4y+9 3x+7 82 M Axis of symmetry Vertex

  9. Theorems Theorem 4.3: Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angle is congruent. How? B O A M C N Statement Reason Given Given Definition Triangle Sum Theorem Triangle Sum Theorem Substitution Substitution Subtraction Definition Axis of symmetry Vertex

  10. Theorems Theorem 4.4: Properties of Congruent Triangles Reflexive Property For any triangle, ΔABC ≅ΔABC Symmetric Property If ΔABC ≅ΔDEF, then ΔDEF ≅ΔABC Transitive Property If ΔABC ≅ΔDEF and ΔDEF ≅ΔGHI, then ΔABC ≅ΔGHI Axis of symmetry Vertex

  11. On your own Assuming congruence, solve for x 4x+7 O 79 M Axis of symmetry Vertex

  12. On your own Assuming congruence, solve for y 51 O 3y+9 M Axis of symmetry Vertex

  13. On your own Assuming congruence, solve for y 25 3y-2 Axis of symmetry Vertex

  14. On your own Assuming congruence, solve for x 45-2x 3x+5 Axis of symmetry Vertex

  15. On your own Assuming congruence, solve for x 4x-5 45-2x 2x 2x-2 Axis of symmetry Vertex

  16. Homework • 4.2 • 1-14

  17. Most Important Points • Basis of comparing congruency

  18. Example Assuming congruence, solve for x &y 52o 6x+6yo 4x+yo 84o Axis of symmetry Vertex

  19. Homework • 4.2 • 15, 16, 19-25

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