Lesson 5-4 The Triangle Inequality. Ohio Content Standards:

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Presentation transcript:

Lesson 5-4 The Triangle Inequality

Ohio Content Standards:

Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two- dimensional figures and three-dimensional objects.

Ohio Content Standards: Use coordinate geometry to represent and examine the properties of geometric figures.

Ohio Content 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 5.11 Triangle Inequality Theorem

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.

6 ½, 6 ½, 14 ½

Determine whether the given measures can be the lengths of the sides of a triangle. 6.8, 7.2, 5.1

A. 7B. 9 C. 11D. 13

Theorem 5.12

The perpendicular segment from a point to a line is the shortest segment from the point to the line.

Theorem 5.12 The perpendicular segment from a point to a line is the shortest segment from the point to the line. AB P shortest distance

Corollary 5.1

The perpendicular segment from a point to a plane is the shortest segment from the point to the plane.

Assignment: Pgs evens, evens