Transcript Lesson 1 Contents

Lesson 5-4
The Triangle Inequality
5-Minute Check on Lesson 5-3
Transparency 5-4
Write the assumption you would make to start an indirect proof of
each statement.
1. ABC  DEF
2. RS is an angle bisector.
3. X is a right angle.
4. If 4x – 3  9, then x  3.
5. MNO is an equilateral triangle.
6.
Which statement is a contradiction to the
statement that W and V are vertical angles?
B mW = 85
A W  V
Standardized Test Practice:
C
mW > mV
D
W is acute
5-Minute Check on Lesson 5-3
Transparency 5-4
Write the assumption you would make to start an indirect proof of
each statement.
1. ABC  DEF
ABC ≇ DEF
2. RS is an angle bisector.
3. X is a right angle.
RS is not an angle bisector.
X is not a right angle.
4. If 4x – 3  9, then x  3.
x>3
5. MNO is an equilateral triangle.
6.
MNO is not an equilateral triangle.
Which statement is a contradiction to the
statement that W and V are vertical angles?
B mW = 85
A W  V
Standardized Test Practice:
C
mW > mV
D
W is acute
Objectives
• Apply the Triangle Inequality Theorem
• Determine the shortest distance between a
point and a line
Vocabulary
• No new vocabulary words or symbols
Theorems & Corollaries
• Theorem 5.11, Triangle Inequality Theorem –
The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.
• Theorem 5.12 – The perpendicular segment
from a point to a line is the shortest segment
from the point to the line.
• Corollary 5.1 – The perpendicular segment
from a point to a plane is the shortest
segment from the point to the plane.
Triangle Inequality
Can a triangle be made out of these pieces?
7.5
4.4
3.3
Yes
The sum of any two sides is greater than the third.
Determine whether the measures
and
can be lengths of the sides of a triangle.
Answer: Because the sum of two measures is not greater
than the length of the third side, the sides cannot
form a triangle.
Determine whether the measures 6.8, 7.2, and 5.1 can
be lengths of the sides of a triangle.
Check each inequality.
Answer: All of the inequalities are true, so 6.8, 7.2, and
5.1 can be the lengths of the sides of a triangle.
Determine whether the given measures can be
lengths of the sides of a triangle.
a. 6, 9, 16
Answer: no
b. 14, 16, 27
Answer: yes
Triangle Inequality Revisited
Given two sides of a triangle, what can the third be?
In a triangle PQR with RQ = 10 and QP = 14, what can RP be?
Any two sides must be greater than the third, so
QP – RQ < RP < RQ + QP
In numbers
14 – 10 < RP < 10 + 14
4 < RP < 24
Multiple-Choice Test Item
In
and
Which measure cannot be PR?
A 7
B9
C 11
D 13
Read the Test Item
You need to determine which value is not valid.
Solve the Test Item
Solve each inequality to determine the range of values
for PR.
Graph the inequalities on the same number line.
The range of values that fit all three inequalities is
Examine the answer choices. The only value that does not
satisfy the compound inequality is 13 since 13 is greater
than 12.4. Thus, the answer is choice D.
Answer: D
Multiple-Choice Test Item
Which measure cannot
be XZ?
A 3
Answer: D
B9
C 12
D 14
Summary & Homework
• Summary:
– The sum of the lengths of any two sides of a
triangle is greater then the length of the third side.
• Homework:
– pg 264: 15-19, 27-31