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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

Chapter 5

Triangles and Congruence

section 5 1
Section 5-1

Classifying Triangles

triangle
Triangle
  • A figure formed when three noncollinear points are joined by segments
triangles classified by angles
Triangles Classified by Angles
  • Acute Triangle – all acute angles
  • Obtuse Triangle – one obtuse angle
  • Right Triangle – one right angle
triangles classified by sides
Triangles Classified by Sides
  • Scalene Triangle – no sides congruent
  • Isosceles Triangle– at least two sides congruent
  • Equilateral Triangle – all sides congruent (also called equiangular)
section 5 2
Section 5-2

Angles of a Triangle

angle sum theorem
Angle Sum Theorem
  • The sum of the measures of the angles of a triangle is 180.
theorem 5 2
Theorem 5-2
  • The acute angles of a right triangle are complementary.
theorem 5 3
Theorem 5-3
  • The measure of each angle of an equiangular triangle is 60.
section 5 3
Section 5-3

Geometry in Motion

translation
Translation
  • When you slide a figure from one position to another without turning it.
  • Translations are sometimes called slides.
reflection
Reflection
  • When you flip a figure over a line.
  • The figures are mirror images of each other.
  • Reflections are sometimes called flips.
rotation
Rotation
  • When you turn the figure around a fixed point.
  • Rotations are sometimes called turns.
pre image and image
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.
mapping
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.
section 5 4
Section 5-4

Congruent Triangles

congruent triangles
Congruent Triangles
  • If the corresponding parts of two triangles are congruent, then the two triangles are congruent
corresponding parts
Corresponding Parts
  • The parts of the congruent triangles that “match”
congruence statement
Congruence Statement
  • Δ ABC ≅Δ FDE
  • The order of the vertices indicates the corresponding parts
cpctc
CPCTC
  • If two triangles are congruent, then the corresponding parts of the two triangles are congruent
  • CPCTC – corresponding parts of congruent triangles are congruent
section 5 5
Section 5-5

SSS and SAS

postulate 5 1
Postulate 5-1
  • If three sides of one triangle are congruent to three corresponding sides of another triangle, then the triangles are congruent. (SSS)
included angle
Included Angle
  • The angle formed by two given sides is called the included angle of the sides
postulate 5 2
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)
section 5 6
Section 5-6

ASA and AAS

postulate 5 3
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.
theorem 5 4
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.
ad