Chapter 5
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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

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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.


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