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Geom 4point1

Geom 4point1






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    Geom 4point1 Geom 4point1 Presentation Transcript

    • 4.1 Triangles and Angles Objectives: - Classify triangles by their sides and angles - Find angle measures
    • Names of Triangles - by sides
      • Equilateral
        • 3 congruent sides
      • Isosceles
        • At least 2 congruent sides
      • Scalene
        • No congruent sides
    • Names of Triangles - by angles
      • Acute
        • 3 acute angles
      • Equilateral
        • 3 congruent angles
      • Right
        • 1 right angle
      • Obtuse
        • 1 obtuse angle
    • When you classify a triangle...
      • Be as specific as possible.
      • acute scalene
      A B C 65˚ 57˚ 58˚
    • When you classify a triangle...
      • What is this one?
      • obtuse isosceles
    • Terms
      • Each of the 3 points joining the sides of a triangle is a vertex
      • 2 sides sharing a common vertex are adjacent sides
      A B C
    • Right Triangles
      • In a right triangle, the side opposite the right angle is called the hypotenuse
      • The sides opposite the two acute angles are called legs
      A B C 50° q r s
    • Isosceles Triangles
      • If an isosceles triangle has 3 congruent sides, it is equilateral.
      • If an isosceles triangle has 2 congruent sides, the sides are the legs of the triangle, and the 3rd side is the base of the triangle.
    • Identifying parts
      • What kind of triangle is this?
      • isosceles right
      • Which side is the hypotenuse?
      • Which side is the base?
      • Which sides are the legs?
      5” 5” 7”
    • Interior & Exterior Angles
      • Interior angles are inside the triangle.
      • Exterior angles are adjacent to the interior angles.
      • Each vertex has a pair of congruent exterior angles.
    • Triangle Sum Theorem
      • The sum of the measures of the interior angles of a triangle is 180˚.
    • 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.
    • Corollary
      • 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.
    • Classwork
      • Do p. 198 1-15 together