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