lesson 5-2 inequalitiesandtriangles. ohio content standards:
TRANSCRIPT
Lesson 5-2Lesson 5-2
Inequalities Inequalities and and
TrianglesTriangles
Ohio Content Ohio Content Standards:Standards:
Ohio Content Ohio Content Standards:Standards:
Formally define geometric figures.
Ohio Content Ohio Content Standards: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 Ohio Content Standards:Standards:
Use algebraic representations, such as
tables, graphs, expressions, functions
and inequalities, to model and solve problem
situations.
Ohio Content Ohio Content Standards:Standards:
Solve equations and inequalities having
rational expressions as coefficients and
solutions.
Definition of InequalityDefinition of Inequality
Definition of InequalityDefinition 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 InequalityDefinition 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 12
Theorem 5.8Theorem 5.8Exterior Angle Exterior Angle
Inequality TheoremInequality Theorem
Theorem 5.8Theorem 5.8Exterior Angle Exterior Angle
Inequality TheoremInequality 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.
1 3
2
4
C
B
A
14 mm
24 mm
Theorem 5.8Theorem 5.8Exterior Angle Exterior Angle
Inequality TheoremInequality Theorem
Use the Exterior Angle Inequality to list all of the angles that satisfy the
stated condition.
12
3 4 5 6
7
12
8
910
11
141516
17
Use the Exterior Angle Inequality to list all of the angles that satisfy the
stated condition.
all angles whose measures are less than m 14
12
3 4 5 6
7
12
8
910
11
141516
17
Use the Exterior Angle Inequality to list all of the angles that satisfy the
stated condition.
all angles whose measures are greater than m 5
12
3 4 5 6
7
12
8
910
11
141516
17
Theorem 5.9Theorem 5.9
Theorem 5.9Theorem 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.
R
U
TS
V5.1
5.3
5.2 6.6
4.43.6 4.8
Determine the relationship between the measures of the
given angles.
R
U
TS
V5.1
5.3
5.2 6.6
4.43.6 4.8
SURRSU ,
Determine the relationship between the measures of the
given angles.
R
U
TS
V5.1
5.3
5.2 6.6
4.43.6 4.8
STVTSV ,
Determine the relationship between the measures of the
given angles.
R
U
TS
V5.1
5.3
5.2 6.6
4.43.6 4.8
RUVRSV ,
Theorem 5.10Theorem 5.10
Theorem 5.10Theorem 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?
X
ZY
16 16
22.6
Assignment:Assignment:
Pgs. 252-254 Pgs. 252-254 18-34 evens, 18-34 evens, 38-42 evens38-42 evens