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Chapter 5

Chapter 5. Triangles and Congruence. Section 5-1. Classifying Triangles. Triangle. A figure formed when three noncollinear points are joined by segments. Triangles Classified by Angles. Acute Triangle – all acute angles Obtuse Triangle – one obtuse angle

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Chapter 5

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  1. Chapter 5 Triangles and Congruence

  2. Section 5-1 Classifying Triangles

  3. Triangle • A figure formed when three noncollinear points are joined by segments

  4. Triangles Classified by Angles • Acute Triangle – all acute angles • Obtuse Triangle – one obtuse angle • Right Triangle – one right angle

  5. Triangles Classified by Sides • Scalene Triangle – no sides congruent • Isosceles Triangle– at least two sides congruent • Equilateral Triangle – all sides congruent (also called equiangular)

  6. Section 5-2 Angles of a Triangle

  7. Angle Sum Theorem • The sum of the measures of the angles of a triangle is 180.

  8. Theorem 5-2 • The acute angles of a right triangle are complementary.

  9. Theorem 5-3 • The measure of each angle of an equiangular triangle is 60.

  10. Section 5-3 Geometry in Motion

  11. Translation • When you slide a figure from one position to another without turning it. • Translations are sometimes called slides.

  12. Reflection • When you flip a figure over a line. • The figures are mirror images of each other. • Reflections are sometimes called flips.

  13. Rotation • When you turn the figure around a fixed point. • Rotations are sometimes called turns.

  14. Pre-image and Image • Each point on the original figure is called a pre-image. • Its matching point on the corresponding figure is called its image.

  15. Mapping • Each point on the pre-image can be paired with exactly one point on the image, and each point on the image can be paired with exactly one point on the pre-image.

  16. Section 5-4 Congruent Triangles

  17. Congruent Triangles • If the corresponding parts of two triangles are congruent, then the two triangles are congruent

  18. Corresponding Parts • The parts of the congruent triangles that “match”

  19. Congruence Statement • Δ ABC ≅Δ FDE • The order of the vertices indicates the corresponding parts

  20. CPCTC • If two triangles are congruent, then the corresponding parts of the two triangles are congruent • CPCTC – corresponding parts of congruent triangles are congruent

  21. Section 5-5 SSS and SAS

  22. Postulate 5-1 • If three sides of one triangle are congruent to three corresponding sides of another triangle, then the triangles are congruent. (SSS)

  23. Included Angle • The angle formed by two given sides is called the included angle of the sides

  24. Postulate 5-2 • If two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. (SAS)

  25. Section 5-6 ASA and AAS

  26. Postulate 5-3 • If two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent.

  27. Theorem 5-4 • If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and nonincluded side of another triangle, then the triangles are congruent.

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