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Congruent Triangles

Chapter 4.3 Congruent Triangles Objective: Understand corresponding parts of congruent triangles and prove congruence by the definition. Check.4.38 Use the principle that corresponding parts of congruent triangles are congruent to solve problems.

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Congruent Triangles

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  1. Chapter 4.3 Congruent TrianglesObjective: Understand corresponding parts of congruent triangles and prove congruence by the definition. Check.4.38 Use the principle that corresponding parts of congruent triangles are congruent to solve problems. CLE 3108.4.8 Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual applications, and transformations. Spi.4.11 Use basic theorems about similar and congruent triangles to solve problems. Spi.4.12 Solve problems involving congruence, similarity, proportional reasoning and/or scale factor of two similar figures or solids.

  2. Congruent Triangles • ALL corresponding parts of congruent triangles are congruent • ABC  FDE D F A E C B

  3. Name the corresponding congruent angles and sides R Q T QRS  RTV Q  T QRS  TRV S  V QR  TR QS  TV SR  VT V S

  4. Properties of Triangle Congruence • Reflexive • Symmetric • Transitive • KLS  KLS • If KLJ  QPR then QPR  KLJ • If KLJ  QPR and QPR  XYZ then KLJ  XYZ L P L L L Y P Z S S J R R J X K K K Q K Q

  5. Transformations of Congruent Triangles • LMN  QRP M L N

  6. Verify that CDE  C’D’E’ C(-5,7) D (-8,6) E(-3,3) • C’(5,7) D’(8,6) E’(3,3) C C’ D’ D E’ E

  7. Prove the Transitive Property Given: If KLJ  QPR and QPR  XYZ Prove: KLJ  XYZ Statements Reasons Given Corresponding parts of congruent angles are congruent (CPCTC) Given CPCTC Transitive Property of angles Transitive Property of segments Def of congruent triangles L P Y • KLJ  QPR • K Q, LP, JR, KJQR, KLQP, LJPR • QPR  XYZ • Q X, PY, RZ, QRXZ, QPXY, PRYZ • K X, LY, JZ • KJXZ, KLXY, LJYZ • KLJ  XYZ J R Z K Q X

  8. Constructions – Congruent Triangles Using Sides Y • Draw a triangle, label the vertices X, Y, and Z • Elsewhere on the paper, use a straight edge to construct segment RS Such that RS  XZ • Using R as the center, draw and arc with radius equal to XY • Using S as the center draw and arc with a radius equal to YZ. • Let T be the point of intersection of the two arcs. • Draw RT and ST to form RST Z X T R S

  9. Constructions – Congruent Triangles using 2 sides and an included angle C A • Draw a triangle, label the vertices A, B, and C • Elsewhere on the paper, use a straight edge to construct segment KL Such that KL  BC • Construct and angle congruent to B using KL as a side of the angle and K as the vertex. • Construct JK such that JK  BA. • Draw JL to complete KJL B J K L

  10. Practice Assignment • Block Page 257 10-22 even and 28 • Honors: page 258 10 – 20 even, 24, 28, 32, 40

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