Chapter 4 Congruent Triangles

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