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Triangle Theorems and Congruent Triangles

Learn about the angle sum and exterior angle theorems, as well as how to prove congruent triangles using SSS, SAS, ASA, AAS, and HL postulates.

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Triangle Theorems and Congruent Triangles

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  1. Unit 4 TRIANGLE FUN 

  2. I can use the angle sum theorem • I can use the angle sum theorem • I can the exterior angle theorem • I can the exterior angle theorem Learning Targets Lesson 4-1

  3. sum angles 180°

  4. 30° m∠1 = 28° m∠1 = 120°

  5. 58° 32° 32° 58° m∠1 = 56° m∠2 = 56° m∠3 = 74°

  6. remote interior exterior not

  7. exterior angle sum remote interior angles m∠1 = m∠A + m∠B

  8. m∠1 = 115°

  9. 2x + 95 = 145 2x = 50 x = 25

  10. 140° 65° 40° 75° 115°

  11. 55° 55° 70°

  12. 125° 55° 95°

  13. ASSIGNMENT: 4-1Worksheet

  14. 4.2 Congruent Triangles Learning Target: • I can name and label corresponding parts of congruent triangles.

  15. vertices A B C

  16. size shape

  17. Angle Measure Betweenness Collinearity Distance

  18. m∠A = m∠J JK AB = m∠B = m∠K BC = KL m∠L JL m∠C = AC = Match up the letters in the same “position” AND look at the ‘tick marks’ in the picture! Match the congruent pieces!

  19. Warm Up

  20. I can recognize and use the SSS, SAS, ASA, AAS, and HL Postulates to see if triangles are the same. Lesson 4.3

  21. CAN’T USE!!! 40 40 50 50

  22. CAN’T USE!!! 7 7 6 6 40° 40°

  23. SAS ∆DNV ≅ ∆BCX

  24. SSS ∆TRS ≅ ∆SUT

  25. HL ∆JKL ≅ ∆MNP

  26. AAS ∆NJK ≅ ∆LMK

  27. Your turn! Try e-h! SAS ∆CDA ≅ ∆BDA

  28. ASA ∆RST ≅ ∆UVT

  29. AAS ∆RUT ≅ ∆RST

  30. SAS ∆FJH ≅ ∆GHJ

  31. A M R C W G MG ≅ AC

  32. D X G K Y Z YZ ≅ DK

  33. D A E F B C ∠B ≅ ∠E or ∠C ≅ ∠F

  34. ASSIGNMENT: “Swimming through triangles” worksheet, both sides (Pages 3 – 4)

  35. Warm Up

  36. PROOFS! Lesson 4.4

  37. TS ≅ TS Given Given Reflexive ∆RST ≅ ∆UTS SSS

  38. US ≅ US Given Given Def’n of angle bisector ∠RSU ≅ ∠TSU Reflexive SAS ∆RSU ≅ ∆TSU

  39. Your Turn…

  40. BD ≅ BD Given Given Reflexive SSS ∆ABD ≅ ∆CBD CPCTC ∠A ≅ ∠C

  41. DF ≅ DF DG ≅ FE Given Given Reflexive AIA ≅↔ || lines ∠EDF ≅ ∠GFD AAS ∆EDF ≅ ∆GFD CPCTC

  42. BC ≅ BC Given Given Reflexive HL ∆BAC ≅ ∆BDC CPCTC ∠A ≅ ∠D

  43. BC || AD BD ≅ BD BC ≅ AD Your Turn… Given Given Reflexive AIA ≅↔ || lines ∠CBD ≅ ∠ADB ∆ABD ≅ ∆CDB SAS

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