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Geometry
Notes – Lesson 5.5
Name _______________________________
Comparison Property of Inequality. If a = b + c and c> 0, then _________
Corollary to the Triangle Exterior Angle Theorem. The measure of an exterior angle
of a triangle is __________________ than the measure of each of its remote interior
angles.
__________ > __________ and _________ > _____________
Example: In the diagram to the left, BC || DE. Why is m4  m3 ?
1.
m4  m2
by ______________________
2.
m2  m3
by _______________________
3.
m4  m3
by _______________________
Theorem 5-10. If two sides of a triangle are not congruent, then the larger _____________ lies
opposite the longer ___________. If XZ > XY ,
then mY  m __________
Examples: List the angles of the triangle in order from smallest to largest.
1.
3. PO
2.
= 38, RO = 26, PR = 28
Theorem 5-11. If two angles of a triangle are not congruent, then the longer ___________ lies
opposite the larger ______________. If
mA  mB , then BC > ________
Examples: List the sides in order from shortest to longest
4.
5.
6.
Theorem 5-12 Triangle Inequality Theorem. The sum of the lengths of any 2 sides of a triangle is
__________ than the length of the ___________ side.
XY + YZ > ________ and YZ + ZX > _________
and ZX + XY > __________
Example: Can a triangle have sides with the given lengths?
4. 4m, 7m, and 8m
5. 6m, 10m, and 17m
6. 2.5m, 3.5m, and 6m
Example: If a triangle has two sides with lengths as given, Describe possible lengths of the third side.
7. 4in., 7 in.
8. 11m, 20m
9. 24in., 37in.