Download Lesson 5-2 - Elgin Local Schools

Lesson 5-2
Inequalities
and
Triangles
Ohio Content
Standards:
Ohio Content
Standards:
Formally define
geometric figures.
Ohio Content
Standards:
Formally define and explain
key aspects of geometric
figures, including:
a. interior and exterior angles
of polygons;
b. segments related to
triangles (median, altitude,
midsegment);
c. points of concurrency
related to triangles (centroid,
incenter, orthocenter, and
circumcenter);
Ohio Content
Standards:
Use algebraic
representations, such as
tables, graphs,
expressions, functions
and inequalities, to model
and solve problem
situations.
Ohio Content
Standards:
Solve equations and
inequalities having
rational expressions as
coefficients and
solutions.
Definition of Inequality
Definition of Inequality
For any real
numbers a and b,
a > b if and only if
there is a positive
number c such that
a = b + c.
Definition of Inequality
For any real
numbers a and b,
a > b if and only if
there is a positive
number c such that
a = b + c.
Example: If 6 = 4 + 2,
6 > 4 and 6 > 2
Determine which angle has the
greatest measure.
5
4
3
2
1
Theorem 5.8
Exterior Angle
Inequality Theorem
Theorem 5.8
Exterior Angle
Inequality Theorem
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.
Theorem 5.8
Exterior Angle
Inequality Theorem
B
2
A
1
3
4
C
m4  m1
m4  m2
Use the Exterior Angle Inequality to
list all of the angles that satisfy the
stated condition.
17
16
5
3 4
11
10
12
9
2
1
8
6
7
14
15
Use the Exterior Angle Inequality to
list all of the angles that satisfy the
stated condition.
17
16
5
3 4
11
10
12
9
2
1
8
6
14
15
7
all angles whose measures are less
than m 14
Use the Exterior Angle Inequality to
list all of the angles that satisfy the
stated condition.
17
16
5
3 4
11
10
12
9
2
1
8
6
14
15
7
all angles whose measures are
greater than m 5
Theorem 5.9
Theorem 5.9
If one side of a
triangle is longer
than another side,
then the angle
opposite the longer
side has a greater
measure than the
angle opposite the
shorter side.
Determine the relationship
between the measures of the
given angles.
5.2
R
5.3
S
3.6
U
6.6
T
4.8
5.1
4.4
V
Determine the relationship
between the measures of the
given angles.
5.2
R
5.3
S
3.6
U
6.6
T
4.8
5.1
4.4
V
RSU , SUR
Determine the relationship
between the measures of the
given angles.
5.2
R
5.3
S
3.6
U
6.6
T
4.8
5.1
4.4
V
TSV , STV
Determine the relationship
between the measures of the
given angles.
5.2
R
5.3
S
3.6
U
6.6
T
4.8
5.1
4.4
V
RSV , RUV
Theorem 5.10
Theorem 5.10
If one angle of a
triangle has a
greater measure
than another
angle, then the
side opposite the
greater angle is
longer that the
side opposite the
lesser angle.
Ebony is following directions for folding a
handkerchief to make a bandana for her
hair. After she folds the handkerchief in
half, the directions tell her to tie the two
smaller angles of the triangle under her
hair. If she folds the handkerchief with
the dimensions shown, which two ends
should she tie?
22.6
Y
16
Z
16
X
Assignment:
Pgs. 252-254
18-34 evens,
38-42 evens