triangles and congruence. classifying triangles a figure formed when three noncollinear points are...
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Chapter 5Triangles and Congruence
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Section 5-1Classifying Triangles
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A figure formed when three noncollinear points are joined by segments
Triangle
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Acute Triangle – all acute angles
Obtuse Triangle – one obtuse angle
Right Triangle – one right angle
Triangles Classified by Angles
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Scalene Triangle – no sides congruent
Isosceles Triangle – at least two sides congruent
Equilateral Triangle – all sides congruent (also called equiangular)
Triangles Classified by Sides
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Section 5-2Angles of a
Triangle
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The sum of the measures of the angles of a triangle is 180.
Angle Sum Theorem
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The acute angles of a right triangle are complementary.
Theorem 5-2
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The measure of each angle of an equiangular triangle is 60.
Theorem 5-3
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Section 5-3Geometry in
Motion
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When you slide a figure from one position to another without turning it.
Translations are sometimes called slides.
Translation
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When you flip a figure over a line.
The figures are mirror images of each other.
Reflections are sometimes called flips.
Reflection
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When you turn the figure around a fixed point.
Rotations are sometimes called turns.
Rotation
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Each point on the original figure is called a pre-image.
Its matching point on the corresponding figure is called its image.
Pre-image and Image
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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.
Mapping
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Section 5-4Congruent Triangles
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If the corresponding parts of two triangles are congruent, then the two triangles are congruent
Congruent Triangles
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The parts of the congruent triangles that “match”
Corresponding Parts
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Δ ABC ≅ Δ FDEThe order of the vertices indicates the corresponding parts
Congruence Statement
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If two triangles are congruent, then the corresponding parts of the two triangles are congruent
CPCTC – corresponding parts of congruent triangles are congruent
CPCTC
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Section 5-5SSS and SAS
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If three sides of one triangle are congruent to three corresponding sides of another triangle, then the triangles are congruent. (SSS)
Postulate 5-1
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The angle formed by two given sides is called the included angle of the sides
Included Angle
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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)
Postulate 5-2
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Section 5-6ASA and AAS
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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.
Postulate 5-3
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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.
Theorem 5-4