5-5 Inequalities in Triangles
10
Goal: to use inequalities involving angles and sides of triangles Activities: 1.Open GSP 4.06 and complete all steps and answer all questions for GSP Triangle Inequality Activity. 2.View Lesson 5-5 Powerpoint and take notes. 3.Work through the following links 1.Khan Academy 2.Rags to Riches 3.Quia 4.Visual Representation 4.Summary: In your notes, explain the three concepts explored in class today relating measures of sides and angles in triangles.
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5-5 Inequalities in Triangles. Activities: Open GSP 4.06 and complete all steps and answer all questions for GSP Triangle Inequality Activity. View Lesson 5-5 Powerpoint and take notes. Work through the following links Khan Academy Rags to Riches Quia Visual Representation - PowerPoint PPT Presentation
Transcript of 5-5 Inequalities in Triangles
Goal: to use inequalities involving angles and sides of trianglesActivities:1.Open GSP 4.06 and complete all steps and answer all questions for GSP Triangle Inequality Activity. 2.View Lesson 5-5 Powerpoint and take notes.3.Work through the following links
1. Khan Academy2. Rags to Riches3. Quia4. Visual Representation
4.Summary: In your notes, explain the three concepts explored in class today relating measures of sides and angles in triangles.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side
Inequalities in One Triangle
6
3 2
6
3 3
4 3
6
Note that there is only one situation that you can have a triangle; when the sum of two sides of the triangle are greater than the third.
They have to be able to reach!!
Triangle Inequality Theorem
AB + BC > AC
A
B
C
AB + AC > BC
AC + BC > AB
Triangle Inequality Theorem
A
B
C
Biggest Side Opposite Biggest AngleMedium Side Opposite
Medium AngleSmallest Side Opposite
Smallest Angle
3
5
m<B is greater than m<C
Triangle Inequality Theorem
Converse is true alsoBiggest Angle Opposite _____________Medium Angle Opposite
______________Smallest Angle Opposite
_______________ B
C
A
65
30
Angle A > Angle B > Angle C
So CB >AC > AB
Example: List the measures of the sides of the triangle, in order of least to greatest.
10x - 10 = 180
Solving for x:
B
A
C
Therefore, BC < AB < AC
<A = 2x + 1 <B = 4x
<C = 4x -11
2x +1 + 4x + 4x - 11 =180
10x = 190
X = 19
Plugging back into our Angles:
<A = 39o; <B = 76; <C = 65
Note: Picture is not to scale
Using the Exterior Angle Inequality
Example: Solve the inequality if
AB + AC > BC
x + 3
x + 2
A
B
C(x+3) + (x+ 2) > 3x - 2
3x - 22x + 5 > 3x - 2
x < 7
Example: Determine if the following lengths are legs of triangles
A) 4, 9, 5
4 + 5 ? 9
9 > 9
We choose the smallest two of the three sides and add them together. Comparing the sum to the third side:
B) 9, 5, 5
Since the sum is not greater than the third side, this is not a
triangle
5 + 5 ? 9
10 > 9Since the sum is greater than the third side, this is
a triangle
Example: a triangle has side lengths of 6 and 12; what are the possible lengths of the third
side?
B
A
C
6 12
X = ?
12 + 6 = 18
12 – 6 = 6Therefore: 6 < X < 18
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