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Chapter 4 Congruent Triangles

Chapter 4 Congruent Triangles. Sec. 4 – 1 Congruent Figures. Objective: 1) To recognize  figures & their corresponding parts. Congruent Polygons. Are the same size and the same shape. Fit exactly on top of each other Have  corresponding parts: Matching sides and s.

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Chapter 4 Congruent Triangles

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  1. Chapter 4Congruent Triangles Sec. 4 – 1 Congruent Figures Objective: 1) To recognize  figures & their corresponding parts

  2. Congruent Polygons • Are the same size and the same shape. • Fit exactly on top of each other • Have  corresponding parts: • Matching sides and s

  3. You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another turn slide

  4. You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another flip flip These are called translations and are covered in chapter 9

  5. You can make 3 kinds of moves so that one congruent figure can fit exactly on top of top of another slide

  6. turn

  7. flip flip

  8. ΔQXT ΔPHD Means you can list the corresponding parts without a diagram QX  PH

  9. Naming Polygons • Order Matters!! When naming, always list cooresponding points in order C B U T AB  ED  B  D  A  WU RS U S W A W R S E D ABCDE  WUTSR

  10. Example: ΔWYS ΔMKV • mW = 25 • mY = 55 • Find mV K Y 55 M V 25 W 100 S

  11. Example 2: Congruence Statement Finish the following congruence statement: ΔJKL Δ_ _ _ M J ΔJKL  ΔNML L K N

  12. Proof: Th(4-1) If 2 s of one Δ are  to 2 s another Δ, then the third s are also . Given: B  E A  D Prove: C  F A B C D F E

  13. Statements • B  E & A  D • mB + mA + mC = 180 • mE + mD + mF = 180 • 3) mB + mA + mC = • mE + mD + mF • mB + mA + mC = • mB + mA + mF • mC = mF • C  F • Reasons • Given • Def. of Δ • Trans. • 4) Subs. • Subtr. • Def. of 

  14. Example • Proof: Given: GC  GD CN  DN Prove: ΔGCN ΔGDN G D C N

  15. G Show all of the parts are  given 3 sides given reflexive D C N given 3 angles given Thm 4-1

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