Triangles and Congruence Chapter 5 Triangles and Congruence

Classifying Triangles 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.