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Congruent Triangles

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- 1. SECTION 4-3 Congruent Triangles
- 2. ESSENTIAL QUESTIONS How do you name and use corresponding parts of congruent polygons? How do you prove triangles congruent using the deﬁnition of congruence?
- 3. VOCABULARY 1. Congruent: 2. Congruent Polygons: 3. Corresponding Parts: Theorem 4.3 - Third Angles Theorem:
- 4. VOCABULARY 1. Congruent:Two ﬁgures with exactly the same size and shape 2. Congruent Polygons: 3. Corresponding Parts: Theorem 4.3 - Third Angles Theorem:
- 5. VOCABULARY 1. Congruent:Two ﬁgures with exactly the same size and shape 2. Congruent Polygons: All parts of one polygon are congruent to matching parts of another polygon 3. Corresponding Parts: Theorem 4.3 - Third Angles Theorem:
- 6. VOCABULARY 1. Congruent:Two ﬁgures with exactly the same size and shape 2. Congruent Polygons: All parts of one polygon are congruent to matching parts of another polygon 3. Corresponding Parts: The matching parts between two polygons; Corresponding parts have the same position in each polygon Theorem 4.3 - Third Angles Theorem:
- 7. VOCABULARY 1. Congruent:Two ﬁgures with exactly the same size and shape 2. Congruent Polygons: All parts of one polygon are congruent to matching parts of another polygon 3. Corresponding Parts: The matching parts between two polygons; Corresponding parts have the same position in each polygon Theorem 4.3 - Third Angles Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles must be congruent
- 8. CPCTC
- 9. CPCTC The Corresponding Parts of Congruent Triangles are Congruent
- 10. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.
- 11. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI
- 12. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH
- 13. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG
- 14. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF
- 15. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF EA ≅ FJ
- 16. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF EA ≅ FJ ∠A ≅ ∠J
- 17. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF EA ≅ FJ ∠A ≅ ∠J ∠B ≅ ∠I
- 18. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF EA ≅ FJ ∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H
- 19. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF EA ≅ FJ ∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H ∠D ≅ ∠G
- 20. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF EA ≅ FJ ∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H ∠D ≅ ∠G ∠E ≅ ∠F
- 21. EXAMPLE 1 Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. AB ≅ JI BC ≅ IH CD ≅ HG DE ≅ GF EA ≅ FJ ∠A ≅ ∠J ∠B ≅ ∠I ∠C ≅ ∠H ∠D ≅ ∠G ∠E ≅ ∠F Since all corresponding parts are congruent, ABCDE ≅ JIHGF
- 22. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y.
- 23. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. ∠P ≅ ∠O
- 24. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O
- 25. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O 6y = 54
- 26. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O 6y = 54 y = 9
- 27. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O 6y = 54 y = 9 IT ≅ NG
- 28. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O 6y = 54 y = 9 x − 2 y = 7.5 IT ≅ NG
- 29. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O 6y = 54 y = 9 x − 2 y = 7.5 IT ≅ NG x − 2(9) = 7.5
- 30. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O 6y = 54 y = 9 x − 2 y = 7.5 IT ≅ NG x − 2(9) = 7.5 x − 18 = 7.5
- 31. EXAMPLE 2 In the diagram, ∆ITP ≅ ∆NGO. Find the values of x and y. 6y − 14 = 40 ∠P ≅ ∠O 6y = 54 y = 9 x − 2 y = 7.5 IT ≅ NG x − 2(9) = 7.5 x − 18 = 7.5 x = 25.5
- 32. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON
- 33. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON
- 34. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON 1. Given
- 35. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON 1. Given 2. ∠LNM ≅ ∠PNO
- 36. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON 1. Given 2. ∠LNM ≅ ∠PNO 2. Vertical Angles Thm.
- 37. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON 1. Given 2. ∠LNM ≅ ∠PNO 2. Vertical Angles Thm. 3. ∠M ≅ ∠O
- 38. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON 1. Given 2. ∠LNM ≅ ∠PNO 2. Vertical Angles Thm. 3. ∠M ≅ ∠O 3. Third Angle Theorem
- 39. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON 1. Given 2. ∠LNM ≅ ∠PNO 2. Vertical Angles Thm. 3. ∠M ≅ ∠O 3. Third Angle Theorem 4.△LMN ≅△PON
- 40. EXAMPLE 3 Write a two-column proof. Given: ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON Prove: △LMN ≅△PON 1. ∠L ≅ ∠P, LM ≅ PO, LN ≅ PN, MN ≅ ON 1. Given 2. ∠LNM ≅ ∠PNO 2. Vertical Angles Thm. 3. ∠M ≅ ∠O 3. Third Angle Theorem 4.△LMN ≅△PON 4. Def. of congruent polygons
- 41. PROBLEM SET
- 42. PROBLEM SET p. 257 #1-23 odd, 29, 36, 39, 49, 53, 55 “I've always tried to go a step past wherever people expected me to end up.” - Beverly Sills

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