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# 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