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7th Grade Math / Lesson 5: Triangles

TRIANGLES
What will we be learning in this lesson?


  • In this lesson, you will learn about the different types of triangles and some of their properties.
Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


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  • Triangles are classified by the sizes of their angles and sides. Here are six different types of triangles.

    Equilateral triangle: a triangle that has all sides and all angles equal

  • Isosceles triangle: a triangle that has two equal sides and two equal angles


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    Scalene triangle: a triangle that has no equal sides and no equal angles


    Right triangle: a triangle that has a right angle


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Obtuse triangle: a triangle that has one obtuse angle (remember obtuse is greater than 90 degrees)



Acute triangle: a triangle that has all acute angles (remember acute is less than 90 degrees)


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  • Use the definitions of the six triangles to name the triangles that have the given information.
  • Are the following triangles equilateral, isosceles, or scalene?
  1. A.A triangle with sides of 5 inches, 6 inches, and 5 inches.
  2. B.A triangle with angles of 20 degrees, 70 degrees, and 90 degrees.
  3. C.A triangle with sides of 4 feet, 4 feet, and 4 feet.
  • For part A, look for the definition that has two sides that are equal. This would be isosceles.
     

  • For part B, look for the definition that has no equal angles. This would be scalene.
     

  • For part C, look for the definition that has all equal sides. This would be equilateral.

 


TRIANGLES


 

  • Use the definitions of the six triangles to name the triangles that have the given information.
  • Are the following triangles right, obtuse, or acute?
  1. A.A triangle with sides of 104 degrees, 36 degrees, and 40 degrees.
  2. B.A triangle with angles of 20 degrees, 70 degrees, and 90 degrees.
  3. C.A triangle with sides of 60 degrees, 70 degrees, and 50 degrees.
  • For part A, look for the definition that has one angle that is greater than 90 degrees. This would be obtuse.
     

  • For part B, look for the definition that has a 90 degree angle. This would be right.
     

  • For part C, look for the definition that has all angles less than 90 degrees. This would be acute.

 


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  • Go back through the lesson and add up the angles of all of the triangles.

  • Do they all add up to the same number? They should all be adding up to 180 degrees. The angles of a triangle will always add up to 180 degrees.

  • Find the missing angle of the triangle below.


  • We know that all angles of a triangle need to add up to 180 degrees. The two angles that are given add up to 145 degrees. The difference between 180 and 145 is the missing angle.
    180 - 145 = 35
    The missing angle is 35 degrees.


  • Can you distinguish between the types of triangles?
  • Can you find a missing angle of a triangle?
  • Go back to the classroom to get to your homework and any other items you need to attend to.