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. CLE 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.

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

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

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

Transformations of Congruent Triangles  LMN   QRP L M N

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

Statements 1.  KLJ   QPR 2.  K  Q,  L  P,  J  R, KJ  QR, KL  QP, LJ  PR 3.  QPR   XYZ 4.  Q  X,  P  Y,  R  Z, QR  XZ, QP  XY, PR  YZ 5.  K  X,  L  Y,  J  Z 6.KJ  XZ, KL  XY, LJ  YZ 7.  KLJ   XYZ Reasons 1.Given 2.Corresponding parts of congruent angles are congruent (CPCTC) 3.Given 4.CPCTC 5.Transitive Property of angles 6.Transitive Property of segments 7.Def of congruent triangles Prove the Transitive Property Given: If  KLJ   QPR and  QPR   XYZ Prove:  KLJ   XYZ K L J Q P R X Y Z

Constructions – Congruent Triangles Using Sides 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 X Y Z RS T

Constructions – Congruent Triangles using 2 sides and an included angle 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 A B C K L J

Practice Assignment Block Page even and 28 Honors: page – 20 even, 24, 28, 32, 40