Applying Parallel Lines to Polygons

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Applying Parallel Lines to Polygons

• Lesson 3.4
• Pre-AP Geometry

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Objectives

• Classify triangles according to sides and to
  angles.
• State and apply the theorem and the corollaries
  about the sum of the measure of the angles of a
  triangle.
• State and apply the theorem about the measure of
  an exterior angle of a triangle.

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Triangle

• A figure formed by three segments joining three
  non-collinear points. Each of the three points
  is called a vertex of the triangle. The segments
  are the sides of the triangle.

B
A
C
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Classifying Triangles

• There are two ways of classifying triangles
• by their sides
• by their angles

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Equilateral Triangle

• All sides are the same length.

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Isosceles Triangles

• At least two sides are the same length

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Scalene Triangles

• No sides are the same length

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Acute Triangles

• Acute triangles have three acute angles

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Right Triangles

• Right triangles have one right angle

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Obtuse Triangles

• Obtuse triangles have one obtuse angle

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Equiangular Triangle

• Equiangular triangles have all congruent angles.

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Auxiliary Line

• A line, not originally a part of a diagram, that
  is added to more clearly show a relationship.
  Auxiliary lines are usually shown as dashed lines.

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Theorem 3-11

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

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Definition Corollary

• A corollary is a statement which follows
  readily from a previously proven statement,
  typically a mathematical theorem.

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Corollary 1

• If two angles of one triangle are congruent to
  two angles of another triangle, then the third
  angles are congruent.

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Corollary 2

• Each angle of an equiangular triangle has a
  measure of 60.

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Corollary 3

• In a triangle, there can be at most one right
  angle or obtuse angle.

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Corollary 4

• The acute angles of a right triangle are
  complementary.

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Definitions

• Exterior Angle
• An angle that forms a linear pair with one of
  the interior angles of the triangle.
• Remote Interior Angles
• In a triangle, the two angles that are
  non-adjacent to the exterior angle of interest.

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Theorem 3-12

• The measure of an exterior angle of a triangle
  equals the sum of the measures of the two remote
  interior angles.

A
C
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Written Exercises

• Problem Set 3.4,
• p. 97 1, 3, 9, 11, 12, 15, 17 19, 21, 24,
  25, 27 29, 31, 33