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A triangle is a polygon with three sides, three angles, and three vertices. All three sides of a triangle are straight lines. To learn the concepts of area and perimeter of triangles please visit my math lesson plan on area and math lesson plan on perimeter.
For clarification purposes, keep in mind the following:
A triangle with vertices A, B and C can be represented as ΔABC.
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Classification of Triangles Based on Sides
Make sure students understand the following definitions. It's best if they copy down the following information:
Triangles can be classified in the following three categories based on the length of the sides:
- Equilateral Triangle: If all the sides of a triangle are equal then it is called an equilateral triangle. It can be proved that all the angles of an equilateral triangle are also equal.
- Isosceles Triangle: If any two sides of a triangle are equal to each other then the triangle will be called an isosceles triangle. The two angles, formed by the equal sides with the unequal side of the triangle are equal.
- Scalene Triangle: For these types of triangles no sides as well as no angles are equal to each other.
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Classification of Triangles Based on Angles
Since your students are already copying information on types of triangles, have them copy the following information on angles:
Triangles can be classified in the following three categories based on angles:
- Acute Angled Triangle: When all the angles of a triangle are less than 90 degrees, then the triangle is called an acute triangle.
- Right Angled Triangle: If one of the angles is 90 degrees then the triangle will be called a right-angled triangle.
- Obtuse Angled Triangle: One of the angles for these types of triangle is more than 90 degrees.
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Important Properties of Triangles
- The sum of all the angles of a triangle will always be 180 degrees.
- The sum of any two sides of a triangle will always be greater than the third side.
- Any external angle of a triangle will be equal to the sum of the two internal angles, which are not adjacent to it. See the picture below:
External angle C (120 degrees) is equal to the sum of internal angle A (49 degrees) and internal angle B (71 degrees).
- A right-angled triangle follows the pythagoras theorem.
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Procedures for Teaching
- Use a white board, a protractor and a ruler to draw a triangle accurately.
- Explain the concept of triangles by drawing different types of triangle on the board. Students should be able to identify and label the different triangles based on the notes you've given them. Show the students how the sum of all the internal angles is equal to 180 degrees. Use a protractor to measure the angles. Explain the different properties of triangles and have students identify or draw examples on the board.
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Classroom Problems on Triangles
Do these problems as a class before moving forward. Remediate individually, if necessary.
- Calculate the third angle of a triangle with two angles of 120 degrees and 30 degrees. Ans: 30 degrees.
- Two sides of an equilateral triangle are 6 mm long. Find out the length of the third side. Ans: 6 mm.
- One angle of a right angled triangle is 35 degrees. Find out the other two angles. Ans: 55 and 90 degrees.