Triangles and Angles Sec 4.1

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Triangles and Angles Sec 4.1

• GOALS
• To classify triangles by their angles and sides
• To find missing angle measures in triangles

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Triangle
Triangle formed by three line segments that
intersect only at their endpoints.
Vertex B
B
Sides AB CB are adjacent to vertex B
C
A
angle
Side AC is opposite angle B
ABC
The line segments are , , and
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Angle and Side Classifications

• Triangles can be classified by their sides and
  angles.
• By sides
• Scalene - no congruent sides
• Equilateral - three congruent sides
• Isosceles - at least two congruent sides

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Angle and Side Classifications

• Triangles can be classified by their sides and
  angles.
• By angles
• Acute an acute triangle is acute because it has
  three acute angles
• Obtuse an obtuse triangle is obtuse because it
  has one obtuse angle
• Right a right triangle is right because it has
  one right angle
• Equiangular an equiangular triangle has three
  congruent sides

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Lets classify some triangles

• Notice All triangles have at least two acute
  angles so they are classified by the measure of
  the third angle.

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Special triangles

• Right Triangle Isosceles Triangle
• Can you have an isosceles right triangle?
• (the base would be the hypotenuse)

Hypotenuse c
Leg a
Leg
Leg
Leg b
base
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Triangle Sum Theorem

• The sum of the measures of the angles in a
  triangle is 180 degrees

• If x 55, and y 75,
• then z 180 (5575) 50

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Exterior Angles of a Triangle

• Exterior angles are angles that are adjacent to
  the interior angles in a triangle. There are 6
  in total, 3 pairs of congruent angles.
• It is customary to only talk about one exterior
  angle at each vertex.

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Exterior Angles Theorem

• The measure of an exterior angle is equal to the
  sum of the two remote interior angles.
• If x 35 degrees and y 45 degrees, then the
  measure of angle 1 is equal to 80.

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Corollary

• A corollary to a theorem is a statement that can
  be proved easily using a theorem.
• Corollary to the Triangle Sum Theorem
• The acute angles of a right triangle are
  complementary.

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You Try! Find the missing angle measure and
classify each triangle
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Examples

• Find x or y.