Download Section 5.5 Inequalities in Triangles FINDING POSSIBLE SIDE

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript 
Section 5.5 Inequalities in Triangles
Corollary or Theorem
Corollary to the Triangle Exterior Angle Theorem
m<1 >m<2 and m<1 > m<3
Example
<2=30
<3=75
Theorem 5-10: If two sides of a triangle are not
congruent then the larger angles lie opposite the
longer side.
If XZ>XY, THEN m<Y >m <Z
Theorem 5-11: If two angles of a triangle are not
congruent then the longer side lies opposite the
larger angle
If m<A > m<B, then BC > AC
Triangle Inequality Theorem:
The sum of the lengths of any two sides of a
triangle is greater than the length of the third side.
XY+YZ > XZ
YZ+ZX>YX
ZX+XY>ZY
FINDING POSSIBLE SIDE LENGTHS
Let x represent the third side of a
triangle. By the Triangle Inequality
Theorem x is between the difference
and the sum of the other two sides
|a-b| < x < |a+b|
<1=105
Y
X
Z
B
A
C
Y
X
Z
X
a
b
Related documents