Int Math 2 Section 5-5 1011

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Congruent Triangles

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Int Math 2 Section 5-5 1011

  1. 1. SECTION 5-5 Congruent TrianglesMon, Jan 31
  2. 2. ESSENTIAL QUESTION How do you use postulates to identify congruent triangles? Where you’ll see this: Engineering, art, recreationMon, Jan 31
  3. 3. VOCABULARY 1. Congruent Triangles: 2. Side-Side-Side Postulate (SSS): 3. Side-Angle-Side Postulate (SAS):Mon, Jan 31
  4. 4. VOCABULARY 1. Congruent Triangles: Triangles where corresponding sides are the same length and corresponding angles are the same measure 2. Side-Side-Side Postulate (SSS): 3. Side-Angle-Side Postulate (SAS):Mon, Jan 31
  5. 5. VOCABULARY 1. Congruent Triangles: Triangles where corresponding sides are the same length and corresponding angles are the same measure 2. Side-Side-Side Postulate (SSS): When you are given three corresponding sets of sides of the triangles as congruent, then the triangles are congruent 3. Side-Angle-Side Postulate (SAS):Mon, Jan 31
  6. 6. VOCABULARY 1. Congruent Triangles: Triangles where corresponding sides are the same length and corresponding angles are the same measure 2. Side-Side-Side Postulate (SSS): When you are given three corresponding sets of sides of the triangles as congruent, then the triangles are congruent 3. Side-Angle-Side Postulate (SAS): When you are given two corresponding sets of sides and the included angle of the sides as congruent, then the triangles are congruentMon, Jan 31
  7. 7. VOCABULARY 4. Angle-Side-Angle Postulate (ASA): 5. Included Angle: 6. Included Side:Mon, Jan 31
  8. 8. VOCABULARY 4. Angle-Side-Angle Postulate (ASA): When you are given two corresponding angles and the included side of the triangles as congruent, then the triangles are congruent 5. Included Angle: 6. Included Side:Mon, Jan 31
  9. 9. VOCABULARY 4. Angle-Side-Angle Postulate (ASA): When you are given two corresponding angles and the included side of the triangles as congruent, then the triangles are congruent 5. Included Angle: The angle formed between two given sides 6. Included Side:Mon, Jan 31
  10. 10. VOCABULARY 4. Angle-Side-Angle Postulate (ASA): When you are given two corresponding angles and the included side of the triangles as congruent, then the triangles are congruent 5. Included Angle: The angle formed between two given sides 6. Included Side: The side formed between two given anglesMon, Jan 31
  11. 11. VOCABULARY 4. Angle-Side-Angle Postulate (ASA): When you are given two corresponding angles and the included side of the triangles as congruent, then the triangles are congruent 5. Included Angle: The angle formed between two given sides 6. Included Side: The side formed between two given angles These are ways to prove triangles as congruent: SSS, SAS, ASAMon, Jan 31
  12. 12. ACTIVITY Materials: Protractor, rulerMon, Jan 31
  13. 13. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 8 cm long.Mon, Jan 31
  14. 14. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 8 cm long. 2. From one of the endpoints, create a 50° angle.Mon, Jan 31
  15. 15. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 8 cm long. 2. From one of the endpoints, create a 50° angle. 3. Create a line segment at that angle that is 4 cm long.Mon, Jan 31
  16. 16. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 8 cm long. 2. From one of the endpoints, create a 50° angle. 3. Create a line segment at that angle that is 4 cm long. 4. Connect that new endpoint to the other original endpoint you haven’t used.Mon, Jan 31
  17. 17. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 8 cm long. 2. From one of the endpoints, create a 50° angle. 3. Create a line segment at that angle that is 4 cm long. 4. Connect that new endpoint to the other original endpoint you haven’t used. 5. Compare your triangle with some classmates in class tomorrow. What do you notice?Mon, Jan 31
  18. 18. ACTIVITY Materials: Protractor, rulerMon, Jan 31
  19. 19. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 3 cm long.Mon, Jan 31
  20. 20. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 3 cm long. 2. From one of the endpoints, create a 35° angle.Mon, Jan 31
  21. 21. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 3 cm long. 2. From one of the endpoints, create a 35° angle. 3. From the other endpoint, create a 75° angle so the ray points toward the 35° angle.Mon, Jan 31
  22. 22. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 3 cm long. 2. From one of the endpoints, create a 35° angle. 3. From the other endpoint, create a 75° angle so the ray points toward the 35° angle. 4. Connect the two rays if they don’t intersect.Mon, Jan 31
  23. 23. ACTIVITY Materials: Protractor, ruler 1. Draw a line segment that is 3 cm long. 2. From one of the endpoints, create a 35° angle. 3. From the other endpoint, create a 75° angle so the ray points toward the 35° angle. 4. Connect the two rays if they don’t intersect. 5. Compare your triangle with some classmates in class tomorrow. What do you notice?Mon, Jan 31
  24. 24. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. A D B C E FMon, Jan 31
  25. 25. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. A D B C E F YesMon, Jan 31
  26. 26. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. A D B C E F Yes ABC ≅DEFMon, Jan 31
  27. 27. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. A D B C E F Yes ABC ≅DEF SSSMon, Jan 31
  28. 28. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. G H I J K LMon, Jan 31
  29. 29. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. G H I J K L YesMon, Jan 31
  30. 30. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. G H I J K L Yes GHI ≅ JKLMon, Jan 31
  31. 31. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. G H I J K L Yes GHI ≅ JKL SASMon, Jan 31
  32. 32. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. M N O P Q RMon, Jan 31
  33. 33. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. M N O P Q R YesMon, Jan 31
  34. 34. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. M N O P Q R Yes MON ≅PRQMon, Jan 31
  35. 35. EXAMPLE 1 State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why. M N O P Q R Yes MON ≅PRQ ASAMon, Jan 31
  36. 36. EXAMPLE 2 Why is it that Angle-Angle-Angle (AAA) does not give congruent triangles?Mon, Jan 31
  37. 37. EXAMPLE 2 Why is it that Angle-Angle-Angle (AAA) does not give congruent triangles? If all the angles are the same, the sides can be different sizes (similar triangles), like with equilateral trianglesMon, Jan 31
  38. 38. EXAMPLE 2 Why is it that Angle-Angle-Angle (AAA) does not give congruent triangles? If all the angles are the same, the sides can be different sizes (similar triangles), like with equilateral trianglesMon, Jan 31
  39. 39. EXAMPLE 2 Why is it that Angle-Angle-Angle (AAA) does not give congruent triangles? If all the angles are the same, the sides can be different sizes (similar triangles), like with equilateral trianglesMon, Jan 31
  40. 40. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. a. Find the lengths of the missing sides. A O M B N YMon, Jan 31
  41. 41. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. a. Find the lengths of the missing sides. A O M B N Y OB = 3 inMon, Jan 31
  42. 42. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. a. Find the lengths of the missing sides. A O M B N Y OB = 3 in OY = 5 inMon, Jan 31
  43. 43. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. a. Find the lengths of the missing sides. A O M B N Y OB = 3 in OY = 5 in MN = 7 inMon, Jan 31
  44. 44. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. b. Find the measures of the missing angles. A O M B N YMon, Jan 31
  45. 45. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. b. Find the measures of the missing angles. A O M B N Y m∠OBY = 37°Mon, Jan 31
  46. 46. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. b. Find the measures of the missing angles. A O M B N Y m∠OBY = 37° m∠ANM = 23°Mon, Jan 31
  47. 47. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. b. Find the measures of the missing angles. A O M B N Y m∠OBY = 37° m∠ANM = 23° 180 − 37 − 23 =Mon, Jan 31
  48. 48. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. b. Find the measures of the missing angles. A O M B N Y m∠OBY = 37° m∠ANM = 23° 180 − 37 − 23 = 120Mon, Jan 31
  49. 49. EXAMPLE 3 MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in. m∠AMN = 37° and m∠OYB = 23°. b. Find the measures of the missing angles. A O M B N Y m∠OBY = 37° m∠ANM = 23° 180 − 37 − 23 = 120 m∠MAN ≅ m∠BOY = 120°Mon, Jan 31
  50. 50. PROBLEM SETMon, Jan 31
  51. 51. PROBLEM SET p. 214 #1-25 “It is not because things are difficult that we do not dare; it is because we do not dare that they are difficult.” - SenecaMon, Jan 31

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