Lesson 1 - Special Right Triangles
GPS Standards
MM2G1a Determine the lengths of sides of 30˚-60˚-90˚ triangles.
MM2G1b Determine the lengths of sides of 45˚-45˚-90˚ triangles.
MM2G1b Determine the lengths of sides of 45˚-45˚-90˚ triangles.
Essential Questions
What is the relationship between the lengths of the legs of a 45˚-45˚-90˚ triangle and the length of the hypotenuse?
What are the relationships among the lengths of the sides of a 30˚-60˚-90˚ triangle?
What are the relationships among the lengths of the sides of a 30˚-60˚-90˚ triangle?
Learning Objectives
§ Students will be able to determine the lengths of sides of 30˚-60˚-90˚ triangles, given at least the length of one side.
§ Students will be able to determine the lengths of sides of 45˚-45˚-90˚ triangles, given at least the length of one side.
§ Students will be able to find the height of an equilateral triangle, given the side lengths and using 45˚-45˚-90˚ triangles.
§ Students will be able to determine the lengths of sides of 45˚-45˚-90˚ triangles, given at least the length of one side.
§ Students will be able to find the height of an equilateral triangle, given the side lengths and using 45˚-45˚-90˚ triangles.
Vocabulary
45˚-45˚-90˚ Triangle Theorem:
In a 45˚-45˚-90˚ triangle, the hypotenuse is sqrt(2) times as long as each leg.
30˚-60˚-90˚ Triangle Theorem:
In a 30˚-60˚-90˚ triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is sqrt(3) times as long as the shorter leg.
In a 45˚-45˚-90˚ triangle, the hypotenuse is sqrt(2) times as long as each leg.
30˚-60˚-90˚ Triangle Theorem:
In a 30˚-60˚-90˚ triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is sqrt(3) times as long as the shorter leg.
*HINT*
Sometimes it is helpful to solve Special Right Triangles using a table.
The first example on the left shows you how to use this table to solve a 30˚-60˚-90˚ triangle.
The second example demonstrates how you can use a similar table to solve a 45˚-45˚-90˚ triangle.
The first example on the left shows you how to use this table to solve a 30˚-60˚-90˚ triangle.
The second example demonstrates how you can use a similar table to solve a 45˚-45˚-90˚ triangle.
Handouts
lesson1-notes.docx | |
File Size: | 187 kb |
File Type: | docx |
lesson1-practice.docx | |
File Size: | 56 kb |
File Type: | docx |
lessonplan1.docx | |
File Size: | 674 kb |
File Type: | docx |