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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
- Right Triangle – one right angle

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

Angles of a Triangle

Angle Sum Theorem

- The sum of the measures of the angles of a triangle is 180.

Theorem 5-2

- The acute angles of a right triangle are complementary.

Theorem 5-3

- The measure of each angle of an equiangular triangle is 60.

Section 5-3

Geometry in Motion

Translation

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

Reflection

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

Rotation

- When you turn the figure around a fixed point.
- Rotations are sometimes called turns.

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

- 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

Congruent Triangles

Congruent Triangles

- If the corresponding parts of two triangles are congruent, then the two triangles are congruent

Corresponding Parts

- The parts of the congruent triangles that “match”

Congruence Statement

- Δ ABC ≅Δ FDE
- The order of the vertices indicates the corresponding parts

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

SSS and SAS

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

- The angle formed by two given sides is called the included angle of the sides

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

ASA and AAS

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

- 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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