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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 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.