Corresponding parts of congruent figures.

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Introduction into Corresponding parts of congruent figures.

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Corresponding parts of congruent figures.

  1. 1. Chapter 4Chapter 4 Congruent TrianglesCongruent Triangles Sec. 4 – 1Sec. 4 – 1 Congruent FiguresCongruent Figures Objective: 1) To recognize ≅ figures & their corresponding parts
  2. 2. Identifying congruent figuresIdentifying congruent figures  Two geometric figures are congruent ifTwo geometric figures are congruent if they have exactly the same size andthey have exactly the same size and shape.shape. CONGRUENT NOT CONGRUENT
  3. 3. Congruent PolygonsCongruent Polygons  Are the same size and the same shape.Are the same size and the same shape. Fit exactly on top of each otherFit exactly on top of each other  HaveHave ≅≅ corresponding parts:corresponding parts: Matching sides andMatching sides and ∠∠ss
  4. 4. You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another
  5. 5. You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another These are called translations and are covered in chapter 9
  6. 6. You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another
  7. 7. ΔΔQXTQXT ≅≅ ΔΔPHDPHD QXQX ≅≅ PHPH
  8. 8. Naming PolygonsNaming Polygons  Order Matters!!Order Matters!! A B C DE S TU W R ABCDE ≅ WUTSR AB ≅ ED ≅ ∠B ≅ ∠D ≅ ∠A ≅ WU RS ∠U ∠S ∠W
  9. 9. Ex. 1 Naming congruent partsEx. 1 Naming congruent parts  The congruentThe congruent triangles. Write atriangles. Write a congruencecongruence statement. Identify allstatement. Identify all parts of congruentparts of congruent corresponding parts.corresponding parts. E F D R T S
  10. 10. Ex. 1 Naming congruent partsEx. 1 Naming congruent parts  The diagram indicatesThe diagram indicates thatthat ∆DEF∆DEF ≅ ∆RST.≅ ∆RST. The congruent anglesThe congruent angles and sides are asand sides are as follows:follows:  Angles:Angles: ∠∠D≅D≅ ∠∠R,R, ∠∠EE ≅≅ ∠∠S,S, ∠∠F ≅F ≅∠∠TT  Sides DE ≅ RS, EF ≅Sides DE ≅ RS, EF ≅ ST, FD ≅ TRST, FD ≅ TR E F D R T S
  11. 11. Example:Example: ΔΔWYSWYS ≅≅ ΔΔMKVMKV  mm∠∠W = 25W = 25  mm∠∠Y = 55Y = 55  Find mFind m∠∠VV W Y S M K V 25 55 100
  12. 12. Example 2: Congruence StatementExample 2: Congruence Statement Finish the following congruence statement: ΔJKL ≅ Δ_ _ _ K J L M N ΔJKL ≅ ΔNML

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