Download Comparing Measurements of a Triangle

Sect. 5.5
Goal 1
Goal 2
Inequalities in One
Triangle
Comparing Measurements of a
Triangle.
Using the Triangle Inequality.
Comparing Measurements of a Triangle
Theorem
Theorem 5.10
5.10
If one side of a triangle is longer than a
second side, then the angle opposite the
longer side has a greater measure than
the angle opposite the shorter side.
A
7
C
5
8
B
The largest angle in
ABC is A.
Comparing Measurements of a Triangle
Theorem 5.11
If one angle of a triangle has a greater measure
than a second angle, then the side opposite the
greater angle is longer than the side opposite
the lesser angle.
S
107°
R
40°
33°
The longest side in
RST is RT
T
Comparing Measurements of a Triangle
Write the measures of the sides of
the triangle in order from least to
greatest.
B
111°
46°
A
23°
C
Comparing Measurements of a Triangle
Write the measures of
the angles of the
triangle in order from
least to greatest.
U
10
7
T
11
V
Comparing Measurements of a Triangle
Q
a)Name the smallest and largest
angles of PQR.
b) Is QR ≥ 8? Why?
57°
P
8
c) Is PQ < 8? Why?
61°
R
Comparing Measurements of a Triangle
Recall!
Exterior Angle – When sides of a triangle are extended,
exterior angles are adjacent and supplementary to interior
angles.
1 is an exterior angle
3
1
2
Exterior Angle Theorem
An Exterior Angle is equal to the sum of the two
remote interior angles.
1 = 3 + 4
4
Comparing Measurements of a Triangle
Theorem 5.12 Exterior Angle Inequality
If an angle is an exterior angle of a
triangle, then its measure is greater than
the measure of either of its corresponding
remote interior angles.
Using the Triangle Inequality
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.
AB + BC > AC
A
AC + BC > AB
AB + AC > BC
C
B
Using the Triangle Inequality
The Triangle Inequality basically says that
you need long enough sides so that they
reach each other. It is showing the growth
of two segments until they meet. Before they
meet no triangle is formed
Using the Triangle Inequality
Hint - For example would sides of length
4, 5 and 6 form a triangle....?
How about sides of length 4, 11, and 7?
If you are an observant student, then you
noticed that all you have to do is add the
two smallest sides to see if it is larger
than the other!
Using the Triangle Inequality
Arrange the sides of quadrilateral ABCD in order
from smallest to largest.
Using the Triangle Inequality
Which of the following sets of numbers could
represent the lengths of the sides of a triangle?
a) 3, 4, 6
b) 10, 11, 21
c) 2, 6, 9
d) 34, 35, 36
Using the Triangle Inequality
A triangle has one side of 11 inches and
another side of 16 inches.
a) Describe the possible lengths of the
3rd side.
b) Construct a
possible triangle with
the two given sides.
C
12 in
11 in
A
16 in
B
Homework
5.5 6-24 even, 42-46