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Classifying Triangles: Types, Properties, and Examples

In this lesson, we explore the classification of triangles based on their sides and angles, utilizing the triangle inequality theorem. We define key concepts such as polygons and triangles, and learn to identify various types including scalene, isosceles, and equilateral triangles. Practical examples guide students in determining triangle types using side lengths and angle measures. The lesson also includes descriptions of vertex, legs, and angles, and provides exercises to reinforce understanding through classification and sketching of triangles.

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Classifying Triangles: Types, Properties, and Examples

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  1. LESSON 3.2B – CLASSIFYING TRIANGLES Geometry Notes T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem) CGT.5.G.3 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)

  2. Definitions Polygon: A closed figure with three or more sides Triangle: A three-sided polygon whose angles add to 180 degrees Vertices: The points where two sides of a polygon intersect

  3. A B C Name the following based on this triangle: Triangle: Sides: Vertices: Angles: What is the side opposite angle A? What is the angle opposite side AC?

  4. Classifying Triangles by Angles

  5. Classifying Triangles by Sides

  6. X Z Y Right Triangle Hypotenuse – Leg – Side opposite Y: Angle opposite : Angle opposite the hypotenuse: Side opposite the right angle: Name the legs:

  7. A C B Isosceles Triangle Legs – Base Angles – Vertex Angle -

  8. Examples • Classify the following triangles by their sides: • A triangle with sides 5x, 5x, and 5x • A triangle with sides 3, 6, and 7 • A triangle with sides 6, 8, and 8

  9. Examples • Classify the following triangles by their angles: • A triangle with angles 25°, 37°, and 118° • A triangle with angles 60°, 60°, and 60° • A triangle with angles 30°, 60°, and 90°

  10. Examples • Sketch the following triangles.If not possible, write not possible: • An obtuse, scalene triangle • A right, equilateral triangle • An acute, isosceles triangle • An equiangular, isosceles triangle

  11. Example Using the distance formula and the coordinates of triangle ABC, classify the triangle. 1. A(-4, 2) B(2,2) C(2, -3)

  12. NOW YOU TRY… Using the distance formula and the coordinates of triangle ABC, classify the triangle. 2. A( -1, 0) B(0, 3) C(2, -3)

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