1. Right Angles and Ratios Slideshow 40, Mathematics Mr. Richard Sasaki, Room 307

2. ObjectivesObjectives Understand common types of right-angled triangles Understand common types of right-angled triangles See how ratios relate for given angle sizes See how ratios relate for given angle sizes Be able to show that a triangle is right- angled Be able to show that a triangle is right- angled Be able to show whether other triangles are acute or obtuse Be able to show whether other triangles are acute or obtuse

3. Right-Angled Triangles If a triangle has a right-angle it could be or. isosceles scalene Scalene Triangles A scalene triangle is a triangle where no lengths or angles are equal. A commonly known scalene triangle is the 30-60-90 triangle. The purple triangle is also 30-60-90 and edges are in the same ratio.

4. Right-Angled Triangles Isosceles Triangles The only type of isosceles right-angled triangle is the triangle. 45-45-90 An isosceles triangle is a triangle where a pair of lengths and angles are equal. The purple triangle is also 45-45-90 and edges are in the same ratio.

5. AnswersAnswers

6. Testing if Right-Angled Example

7. AnswersAnswers Yes No No No Yes Yes Two of the numbers are even, so it is not right-angled.

8. Acute and Obtuse Triangles An acute triangle exists when. An obtuse triangle exists when. A right-angled triangle exists when. Acute Isosceles Obtuse Isosceles Right-angled Isosceles Acute Scalene Obtuse Scalene Right-angled Scalene

9. Acute and Obtuse Triangles When a triangle is acute… When a triangle is obtuse…

10. Acute and Obtuse Triangles Example obtuse All edges are different so the triangle is obtuse scalene.

11. Answers - Easy Obtuse Isosceles Acute Scalene Right-Angled Scalene Acute Scalene Obtuse Scalene Acute Isosceles Right-Angled Scalene Obtuse Scalene The length of the two shorter edges is less than the longest edge

12. Answers - Hard All angles nearly the same.