Lesson 5-4Lesson 5-4

The Triangle The Triangle InequalityInequality

Ohio Content Ohio Content Standards:Standards:

Ohio Content Ohio Content Standards:Standards:

Describe and apply the properties of similar and congruent figures; and

justify conjectures involving similarity and congruence.

Ohio Content Ohio Content Standards:Standards:

Make and test conjectures about characteristics and

properties (e.g., sides, angles, symmetry) of two-dimensional figures and

three-dimensional objects.

Ohio Content Ohio Content Standards:Standards:

Use coordinate geometry to represent and examine the

properties of geometric figures.

Ohio Content Ohio Content Standards:Standards:

Establish the validity of conjectures about geometric objects, their properties and

relationships by counter-example, inductive and

deductive reasoning, and critiquing arguments made by

others.

Theorem 5.11Theorem 5.11Triangle Inequality Triangle Inequality

TheoremTheorem

Theorem 5.11Theorem 5.11Triangle Inequality Triangle Inequality

TheoremTheorem

The sum of the lengths of any two sides of a

triangle is greater than the length of the third

side.

Determine whether the given measures can be the lengths of

the sides of a triangle.

Determine whether the given measures can be the lengths of

the sides of a triangle.

6 ½, 6 ½, 14 ½6 ½, 6 ½, 14 ½

Determine whether the given measures can be the lengths of

the sides of a triangle.

6.8, 7.2, 5.16.8, 7.2, 5.1

A.A. 77 B. 9B. 9C. 11C. 11 D. D. 1313

? becannot measureWhich

.2.5 and ,2.7 ,In

PR

QRPQPQR

Theorem 5.12Theorem 5.12

Theorem 5.12Theorem 5.12

The perpendicular segment from a point to

a line is the shortest segment from the point

to the line.

Theorem 5.12Theorem 5.12

The perpendicular segment from a point to

a line is the shortest segment from the point

to the line.

A B

P

shortestdistance

Corollary 5.1Corollary 5.1

Corollary 5.1Corollary 5.1

The perpendicular segment from a

point to a plane is the shortest

segment from the point to the plane.

Assignment:Assignment:

Pgs. 264-266 Pgs. 264-266 14-36 evens, 14-36 evens, 42-44 evens42-44 evens