Chapter 5: Relationships Within Triangles

epicbriggs, Feb 22, 2016

Table of Contents

  1. 5-1 Bisectors in Triangles
    1. Perpendicular Bisector Theorem
    2. Angle Bisector Theorem
  2. 5-3 Inequalities in One Triangle
    1. Triangle Exterior Angle
    2. Inequalities in a Triangle - Relationship of Sides to Angles
  3. 5-5 The Triangle Inequality
    1. Triangle Inequality Exploration
  4. 5-6 Inequalities in Two Triangles
    1. Hinge Theorem

1.

5-1 Bisectors in Triangles

  • 1. Perpendicular Bisector Theorem
  • 2. Angle Bisector Theorem

1.1.

Perpendicular Bisector Theorem

Perpendicular Bisector Theorem
Perpendicular Bisector Theorem
– MsMagerGP

1.2.

–

2.

5-3 Inequalities in One Triangle

  • 1. Triangle Exterior Angle
  • 2. Inequalities in a Triangle - Relationship of Sides to Angles

2.1.

Triangle Exterior Angle

[color=#000000]In the app below, an [b]exterior angle of a triangle[/b] is shown.[br]The 2 colored angles[/color][color=#000000] are referred to as its [/color][i]remote interior angles. [/i]
Interact with this app for a few minutes. LARGE POINTS are moveable.
[color=#000000]What can we conclude about the measure of an exterior angle when we compare it to its remote interior angles? Explain. [/color]
What other theorem is readily made obvious here?
– Tim Brzezinski

2.2.

–

3.

5-5 The Triangle Inequality

  • 1. Triangle Inequality Exploration

3.1.

Triangle Inequality Exploration

Triangle Inequality Exploration
Triangle Inequality Exploration
– xlenchik, MathPatty1

4.

5-6 Inequalities in Two Triangles

  • 1. Hinge Theorem

4.1.

Hinge Theorem

Discover the Hinge Theorem.
Hinge Theorem
Complete the Hinge Theorem. [br]If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then ________________________.
– Heidi McCarty

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