Chapter 41 Notes Apply Triangle Sum Properties by hcj

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									      Chapter 4.1 Notes: Apply
      Triangle Sum Properties

Goal: You will classify triangles and find
measures of their angles.
• A triangle is a polygon with three sides.

• A triangle with vertices A, B, and C is called
  “triangle ABC” or “∆ABC.”

Classifying Triangles by Sides
• A scalene triangle is a triangle with no congruent
  sides.

• An isosceles triangle is a triangle with at least two
  congruent sides.
• An equilateral triangle is a triangle with three
  congruent sides.

Classifying Triangles by Angles
• An acute triangle is a triangle with three acute
  angles.

• A right triangle is a triangle with one right angle.

• An obtuse triangle is a triangle with one obtuse
  angle.
• An equiangular triangle is a triangle with three
  congruent angles.

Ex.1: Classify the triangular shape of the support
 beams in the diagram by its sides and by measuring
 its angles.
Ex.2: Classify the triangle shown in the diagram by its
 sides and angles.
Ex.3: Classify the triangle by its sides and angles.
Angles
• When the sides of a polygon are extended, other
  angles are formed.

• The original angles are the interior angles.

• The angles that form linear pairs with the interior
  angles are the exterior angles.
• Theorem 4.1 Triangle Sum Theorem:
  The sum of the measures of the interior angles of a
  triangle is 180o.

• Theorem 4.2 Exterior Angle Theorem:
  The measure of an exterior angle of a triangle is
  equal to the sum of the measures of the two
  nonadjacent interior angles.
Ex.4: Find          .




Ex.5: Find the measure of   in the diagram shown.
• A corollary to a theorem is a statement that can be
  proved easily using the theorem.

• Corollary to the Triangle Sum Theorem:
  The acute angles of a right triangle are
  complementary.
Ex.6: The tiled staircase shown forms a right triangle.
 The measure of one acute angle in the triangle is
 twice the measure of the other. Find the measure of
 each acute angle.
Ex.7: Find




Ex.8: Find the measure of each interior angle of
 ∆ABC, where
Ex.9: Find the measures of the acute angles of the
 right triangle in the diagram shown.

								
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