Grade 10 Mathematics Euclidean Geometry.pptx

The lesson is about Triangles and it's aim is to equip learners with more knowledge about different types of triangles.

1. Grade 10 Mathematics Euclidean Geometry Triangles Presented by Y Fihlani

2. Introduction Welcome, Grade 10 learners, to our mathematics lesson on Euclidean Geometry, focusing on triangles. Today, we’ll explore the fundamental properties of triangles, a crucial aspect of geometry that forms the basis for many other mathematical concepts. Whether you are already familiar with the basics or encountering these ideas for the first time, this lesson will help deepen your understanding of the different types of triangles and their properties.

3. Definition of a triangle Triangle is a shape (polygon) with three straight sides and three angles that all add up to 180 degrees (Ronan, 1984). The lines ABC forms a triangle from the picture given.

4. Types of triangles Triangles are classified into two categories with three types under each category. Based on sides: Under this category there is Equilateral; Isosceles and Scalene triangle. Based on angles: There is Acute; Obtuse and Right-angled triangle Let us observe each of these triangles in detail.

5. Equilateral triangle This type of triangle has all the sides equal. It has three equal angles that are all equal with each equal to 60 degrees and they add up to 180 degrees. The name equilateral is named after its properties that it has both sides and angles equal.

6. Isosceles triangle This is a type of triangle that has two equal sides. It has also two equal angles. The sum of all angles is equal to 180 degrees (sum of angles in a triangle

7. Scalene triangle This type of triangle has three different sides in length meaning that no side is equal to one another. All the angles are different in size. These different angles add up to 180 degrees (sum of angles in a triangle)

8. Acute-angled triangle This is a type of triangle that is based on angles category. All the angles in this triangle are below 90 degrees and greater than zero degrees. The term “acute” means that the angles of a particular triangle are less than 90 degrees

9. Right-angled triangle The name right-angled triangle comes from the fact that this type of triangle has one angle that is equal to 90 degrees. It has hypotenuse which is the longest side of the right-angled triangle and this side is opposite to a 90 degrees angle. The sum of other two interior angles is 90 degrees.

10. Obtuse-angled triangle This type of triangle is classified under based on angles category One of the angles in this triangle is greater than 90 degrees but less than 180 degrees. The term “obtuse” means that an angle in a particular triangle or shape is more than 90 degrees and less than 180 degrees.

11. Summary Equilateral Triangle: All three sides and angles are equal, with each angle measuring 60 degrees. Isosceles Triangle: Two sides are of equal length, and the angles opposite these sides are equal. Scalene Triangle: All three sides and angles are different from one another. Right Triangle: One of the angles is a right angle (90 degrees).Acute Triangle: All three angles are less than 90 degrees. Obtuse Triangle: One of the angles is greater than 90 degrees. These classifications are based on the length of sides (Equilateral, Isosceles, Scalene) and the measure of angles (Right, Acute, Obtuse)

12. Reference list Chilton Primary School. (n.d.). Types of triangles. Available from Power point at https://www.chiltonprimary.co.uk/attachments/download.asp?file=5060&type=pptx (Accessed on 19 August 2024) Grangeton Academy. (2020). Types of triangles. Available from Power point at https://www.grangeton.uk/wp-content/uploads/2020/05/Types-of-Triangle-PowerPoint.pdf (Assessed on 19 August 2024) Ronan, M. A. (1984). Triangle geometries. Journal of Combinatorial Theory, Series A, 37(3), 294-319. SlideShare. (n.d.). Triangles: What are the properties of an isosceles triangle? Available from SlideShare at https://www.slideshare.net/slideshow/triangles-what-are-the-properties-of-an-isosceles-trianglepdf/251927211?from_search=16 (Assessed on 21 August 2024) SlideShare. (n.d.). Triangles. Available from SlideShare at https://www.slideshare.net/slideshow/triangles-249853916/249853916?from_search=4 (Accessed on 18 August 2024) SlideShare. (n.d.). Triangles. Available from SlideShare at https://www.slideshare.net/slideshow/triangles-class-roompresentation-22374757/22374757?from_search=6 (Accessed from 20 August 2024) SlideShare. (n.d.). Types of triangles. Available from SlideShare at https://www.slideshare.net/slideshow/types-of-triangles-119301102/119301102?from_search=0#6 (Accessed on 19 August) Vishnu. (n.d.). Triangles Available from SlideShare at https://www.slideshare.net/slideshow/vishnu-1-39419142/39419142?from_search=1 (Assessed on 19 August 2024)