Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Successfully reported this slideshow.

Like this presentation? Why not share!

- Geometry section 4-1 1112 by Jimbo Lamb 2160 views
- Geometry Section 4-5 1112 by Jimbo Lamb 2741 views
- Geometry Section 4-6 1112 by Jimbo Lamb 2937 views
- Geometry Section 4-2 by Jimbo Lamb 4195 views
- Geometry Section 4-4 1112 by Jimbo Lamb 2120 views
- Geometry Section 3-3 1112 by Jimbo Lamb 2553 views

2,530 views

Published on

Congruent Triangles

No Downloads

Total views

2,530

On SlideShare

0

From Embeds

0

Number of Embeds

1,413

Shares

0

Downloads

8

Comments

0

Likes

1

No embeds

No notes for slide

- 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

No public clipboards found for this slide

Be the first to comment