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# Chapter 5 - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Chapter 5' - kenna

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### Chapter 5

Triangles and Congruence

Classifying Triangles

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

• Acute Triangle – all acute angles

• Obtuse Triangle – one obtuse angle

• Right Triangle – one right angle

• Scalene Triangle – no sides congruent

• Isosceles Triangle– at least two sides congruent

• Equilateral Triangle – all sides congruent (also called equiangular)

Angles of a Triangle

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

• The acute angles of a right triangle are complementary.

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

Geometry in Motion

• When you slide a figure from one position to another without turning it.

• Translations are sometimes called slides.

• When you flip a figure over a line.

• The figures are mirror images of each other.

• Reflections are sometimes called flips.

• When you turn the figure around a fixed point.

• Rotations are sometimes called turns.

• Each point on the original figure is called a pre-image.

• Its matching point on the corresponding figure is called its image.

• 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.

Congruent Triangles

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

• The parts of the congruent triangles that “match”

• Δ ABC ≅Δ FDE

• The order of the vertices indicates the corresponding parts

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

• CPCTC – corresponding parts of congruent triangles are congruent

SSS and SAS

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

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

• 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)

ASA and AAS

• 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.

• 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.