Download Investigation Angle-Side Relationship Theorems Theorem: Example

Geometry Pre-AP
Notes 5.5-5.6
Investigation
Angle-Side Relationship Theorems
Theorem:
Example:
Theorem:
Example:
See if you can identify the largest angles and longest sides….
1. Write the angles of this triangle in order from smallest to largest.
2. Write the sides of this triangle in order from shortest to longest.
A triangle is formed by three segments, but not EVERY set of three segments can form a triangle!
A certain relationship must exist among the lengths of three segments in order for them to form a triangle.
Triangle Inequality Theorem
A
B
Examples….
Triangle Inequality Theorem
Tell whether you can make a triangle with the given side lengths. Explain
1. 3,5,7
2. 4, 6.5, 11
3. n + 5, n2, 2n, where n = 3
Finding Side Lengths of Triangles
1. The lengths of two sides of a triangle are 6 centimeters and 11 centimeters. Find the range of possible
lengths for the third side.
Strategy: Let s represent the possible lengths for the third side. Apply the Triangle Inequality Theorem.
s + 6 > 11
s>5
s + 11 > 6
s > -5
6 + 11 > s
17 > s
Combine the inequalities, and you get 5 < s < 17. So the length so the third side is greater than 5 cm, but
less than 17 cm.
NOTICE….that the smallest number in your range is the difference between 6 and 11, and the largest
number in your range is the sum of 6 and 11.
Example:
Find the value of n such that (n + 1), 2n, and 4n form the side lengths of a triangle.
C
Hinge Theorem
Note: The Converse of the Hinge Theorem is also true!!
Converse:
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Examples: Compare the given measures.
1. AC and XZ
2. m  SRT and m  QRT