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Lesson 4-1

Triangle Fundamentals. Lesson 4-1. B. C. A. Naming Triangles. A triangle is named by using its vertices. For example, we can call the following triangle:. ∆ABC. ∆ACB. ∆BAC. ∆BCA. ∆CAB. ∆CBA. Opposite Sides and Angles. Opposite Sides:. Side opposite to  A :.

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Lesson 4-1

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  1. Triangle Fundamentals Lesson 4-1 Lesson 4-1: Triangle Fundamentals

  2. B C A Naming Triangles A triangle is named by using its vertices. For example, we can call the following triangle: ∆ABC ∆ACB ∆BAC ∆BCA ∆CAB ∆CBA Lesson 4-1: Triangle Fundamentals

  3. Opposite Sides and Angles Opposite Sides: Side opposite to A : Side opposite to B : Side opposite to C : Opposite Angles: Angle opposite to : A Angle opposite to : B Angle opposite to : C Lesson 4-1: Triangle Fundamentals

  4. Equilateral: A A B C C BC = 3.55 cm B BC = 5.16 cm G H I HI = 3.70 cm Classifying Triangles by Sides Scalene: A triangle in which all 3 sides are different lengths. AC = 3.47 cm AB = 3.47 cm AB = 3.02 cm AC = 3.15 cm Isosceles: A triangle in which at least 2 sides are equal. • A triangle in which all 3 sides are equal. GI = 3.70 cm GH = 3.70 cm Lesson 4-1: Triangle Fundamentals

  5. A triangle in which all 3 angles are less than 90˚. G ° 76 ° ° 57 47 H I A ° 44 ° 108 ° 28 C B Classifying Triangles by Angles Acute: Obtuse: • A triangle in which one and only one angle is greater than 90˚& less than 180˚ Lesson 4-1: Triangle Fundamentals

  6. Classifying Triangles by Angles Right: • A triangle in which one and only one angle is 90˚ Equiangular: • A triangle in which all 3 angles are the same measure. Lesson 4-1: Triangle Fundamentals

  7. polygons triangles scalene isosceles equilateral Classification by Sides with Flow Charts & Venn Diagrams Polygon Triangle Scalene Isosceles Equilateral Lesson 4-1: Triangle Fundamentals

  8. polygons triangles right acute equiangular obtuse Classification by Angles with Flow Charts & Venn Diagrams Polygon Triangle Right Obtuse Acute Equiangular Lesson 4-1: Triangle Fundamentals

  9. Theorems & Corollaries Triangle Sum Theorem: The sum of the interior angles in a triangle is 180˚. Third Angle Theorem: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Corollary 1: Each angle in an equiangular triangle is 60˚. Corollary 2: Acute angles in a right triangle are complementary. There can be at most one right or obtuse angle in a triangle. Corollary 3: Lesson 4-1: Triangle Fundamentals

  10. Exterior Angle Theorem The measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Remote Interior Angles A Exterior Angle D Example: Find the mA. B C 3x - 22 = x + 80 3x – x = 80 + 22 2x = 102 mA = x = 51° Lesson 4-1: Triangle Fundamentals

  11. B C F D E A Median - Special Segment of Triangle Definition: A segment from the vertex of the triangle to the midpoint of the opposite side. Since there are three vertices, there are three medians. In the figure C, E and F are the midpoints of the sides of the triangle. Lesson 4-1: Triangle Fundamentals

  12. B B F F D I A D K A Altitude - Special Segment of Triangle The perpendicular segment from a vertex of the triangle to the segment that contains the opposite side. Definition: In a right triangle, two of the altitudes of are the legs of the triangle. In an obtuse triangle, two of the altitudes are outside of the triangle. Lesson 4-1: Triangle Fundamentals

  13. P M Q O R N L D C Perpendicular Bisector – Special Segment of a triangle A line (or ray or segment) that is perpendicular to a segment at its midpoint. Definition: The perpendicular bisector does not have to start from a vertex! Example: A E A B B In the isosceles ∆POQ, is the perpendicular bisector. In the scalene ∆CDE, is the perpendicular bisector. In the right ∆MLN, is the perpendicular bisector. Lesson 3-1: Triangle Fundamentals

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