Triangle. Inequalities

Сентябрь 13, 2022

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Triangle. Inequalities

Содержание

2. Triangle Inequality Theorem: Can you make a triangle? Yes!
3. Triangle Inequality Theorem: Can you make a triangle? NO because 4 + 5
4. Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is
5. Finding the range of the third side: Example Given a triangle with sides of length 3
6. Finding the range of the third side: Given The lengths of two sides of a triangle
7. Finding the range of the third side: Example Given a triangle with sides of length a
8. In a Triangle: The largest angle is opposite the largest side. The smallest angle is opposite
9. Theorem If one angle of a triangle is larger than a second angle, then the side
10. Theorem If one side of a triangle is larger than a second side, then the angle
11. Corollary #1: The perpendicular segment from a point to a line is the shortest segment from
13. Скачать презентацию

Слайд 2

Triangle Inequality Theorem:
Can you make a triangle?
Yes!

Слайд 3

Triangle Inequality Theorem:
Can you make a triangle?
NO
because
4 + 5 < 12

Слайд 4

Triangle Inequality Theorem:
The sum of the lengths of any two sides

of a triangle is greater than the length of the third side.

a + b > c
a + c > b
b + c > a

Слайд 5

Finding the range of the third side:
Example Given a triangle with

sides of length 3 and 7, find the range of possible values for the third side.
Solution Let x be the length of the third side of the triangle.
The maximum value:
x < 3 + 7 = 10
The minimum value:
x > 7 – 3 = 4
So 4 < x < 10 (x is between 4 and 10.)

x < 10

x > 4

Слайд 6

Finding the range of the third side:
Given The lengths of two

sides of a triangle
Since the third side cannot be larger than the other two added together, we find the maximum value by adding the two sides.
Since the third side and the smallest side given cannot be larger than the other side, we find the minimum value by subtracting the two sides.

Difference < Third Side < Sum

Слайд 7

Finding the range of the third side:
Example Given a triangle with

sides of length a and b, find the range of possible values for the third side.
Solution Let x be the length of the third side of the triangle.
The maximum value:
x < a + b
The minimum value:
x > |a – b|
So |a – b|< x < a + b
(x is between |a – b| and a + b.)

x < a + b

x > |a – b|

Слайд 8