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Unit 2

Triangles. Unit 2. Definition of Triangle. A geometric figure formed by three segments joining noncollinear points. B. C. A. Naming Triangles. Triangles are named by using its vertices. For example, we can call the following triangle:. ∆ABC. ∆ACB. ∆BAC. ∆BCA. ∆CAB. ∆CBA.

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Unit 2

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  1. Triangles Unit 2

  2. Definition of Triangle A geometric figure formed by three segments joining noncollinear points .

  3. B C A Naming Triangles Triangles are named by using its vertices. For example, we can call the following triangle: ∆ABC ∆ACB ∆BAC ∆BCA ∆CAB ∆CBA

  4. 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

  5. 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

  6. 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˚

  7. 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.

  8. polygons triangles scalene isosceles equilateral Classification by Sides with Flow Charts & Venn Diagrams Polygon Triangle Scalene Isosceles Equilateral Lesson 3-1: Triangle Fundamentals

  9. polygons triangles right acute equiangular obtuse Classification by Angles with Flow Charts & Venn Diagrams Polygon Triangle Right Obtuse Acute Equiangular

  10. Helpful Triangle Information Triangle Sum: The sum of the interior angles in a triangle is 180˚. Third Angle of a Triangle: If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Fact # 1: Each angle in an equiangular triangle is 60˚. Fact # 2: Acute angles in a right triangle are complementary. There can be at most one right or obtuse angle in a triangle. Fact # 3:

  11. Exterior Angle and Remote Interior Angles Exterior Angle - An angle formed by one side of a triangle and the extension of another side of the triangle. Remote Interior Angles – Interior angles that are not adjacent to the exterior angle of the triangle.

  12. 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 Example: Find the mA. B C 3x - 22 = x + 80 3x – x = 80 + 22 2x = 102 mA = x = 51°

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