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Chapter 4

Chapter 4. Congruent Triangles. 4.2 Apply Congruence and Triangles. Congruent figures- They have exactly the same shape. All parts of one figure are congruent to the corresponding parts of the other figure. Corresponding sides and angles are congruent. Example.

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Chapter 4

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  1. Chapter 4 Congruent Triangles

  2. 4.2 Apply Congruence and Triangles • Congruent figures- • They have exactly the same shape. • All parts of one figure are congruent to the corresponding parts of the other figure. • Corresponding sides and angles are congruent.

  3. Example • Name the congruent triangles.

  4. Example • Find x and y.

  5. Third Angle Theorem • If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are also congruent.

  6. Example

  7. Example

  8. 4.3 Prove Triangles Congruent by SSS • Side-Side-Side Congruence Postulate- If 3 sides of one triangle are congruent to 3 sides of a second triangle, then the two triangles are congruent.

  9. 4.4 Prove Triangles Congruent by SAS and HL • Side- Angle- Side Congruence Postulate – If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of a second triangle, then the 2 triangles are congruent.

  10. Example • R is the center of the circle. Based on the diagram, what can you conclude about ∆URT and ∆SRT ?

  11. Why SSA does not work.

  12. Hypotenuse Leg Congruence Theorem • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the 2 triangles are congruent.

  13. Proof

  14. 4.5 Prove Triangles Congruent by ASA and AAS • Angle- Side- Angle Congruence Postulate- If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of a second triangle, then the 2 triangles are congruent.

  15. Angle- Angle- Side Congruence Theorem- If 2 angle and a non-included side of one triangle are congruent to 2 angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

  16. Right Angle Congruence Theorem- All right angles are congruent.

  17. 4.6 Use Congruent Triangles • CPCTC- Corresponding Parts of Congruent Triangles are Congruent

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