5.5 Inequalities in Triangles
DOM
Can you figure out the puzzle below???
Domino
Comparison Property of Inequality
Comparison Property of Inequality:If a = b + c, and c > 0, then a > b.
a
b c
Theorem
Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.
31 and 21 mmmm
1
3
2
Application
32 mmGiven the figure below, explain why .
21 mm
31 mm
32 mm
Statements Reasons
1.
2.
3.
1.
2.
3.
Theorem
Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
. then ,Z If ZmYmXYX
Example
List the angles of the following figure in order from smallest to largest.
Theorem
Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.
. then ,Am If ACBCBm
Sides of a Triangle
List the sides of the following triangle in order from shortest to longest.
Determine which segment is shortest in the following diagram.
Theorem
Theorem 5-12: Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
XZX YZY YX ZXYZ ZYXZX Y
Theorem
Can a triangle have sides with the given lengths?
a) 7 ft, 3 ft, 8 ft
b) 10 cm, 6 cm, 3 cm
A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side.
5.5 Inequalities in Triangles
HW 5.5: #1-25 (1st column), 32, 33, 35
p.192: #3-4, 11, 22, 24-26ESGGSGEGGEGSSGGE
Can you figure out the puzzle below???
Scrambled Eggs
Proof of Comparison Property of Inequality
Statements Reasons
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
Given: a = b + c, c > 0
Prove: a > b
c > 0b + c > b + 0
b + c > ba = b + c
a > b
Midterm ReviewGiven the figure below, name the type of angle pairs given.
8 and 3 1)
6 and 4 2)
7 and 1 3)
7 and 2 4)
8 and 5 5)
5 and 4 6)
Midterm ReviewFind . Justify each answer.2 and 1 mm
1)
2)
135°
1
2
Midterm ReviewFind x in the following polygon.
125° 125°x°
Midterm Review
Find the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5).
Find the equation of a line that goes through the point (-2, 1) and (3,2).