Triangles

Judith Hilinski, Jul 16, 2019

The Angles of a Triangle Proving that Triangles are Congruent

Table of Contents

  1. The Angles of a Triangle
    1. Basic Definitions: Triangles
    2. Triangles and Their Classification
    3. Symbols and Examples-Angles in Triangles
  2. Triangles Proofs and Theorems
    1. Copy of triangle angle-sum theorem
    2. Triangle Sum Theorem
  3. Practice Problems
    1. Practice Problems with Triangles

1.

The Angles of a Triangle

  • 1. Basic Definitions: Triangles
  • 2. Triangles and Their Classification
  • 3. Symbols and Examples-Angles in Triangles

1.1.

Basic Definitions: Triangles

Simple Closed Curves
[b][color=#ff0000][size=150][size=200]A Simple, Closed Curve is a closed curve that does not [url=https://www.mathopenref.com/intersection.html]intersect[/url] itself. [/size][/size][/color][/b]
Non-example
Not a Simple Closed Curve: figure is closed, but the line of the figure intersects itself several times.
Non-Example
Not a Simple Closed Curve: The line does not intersect itself, but the figure is not closed.
Non-Example
Not a Simple Closed Curve: The line intersects itself, and the figure is not closed.
Example
A Simple Closed Curve: The figure is closed and the line does not intersect itself.
[size=200][size=150][b][color=#ff0000]When a simple closed curve is made up entirely of [/color][color=#0000ff][url=https://www.mathsisfun.com/definitions/line-segment.html]line segments[/url][/color][color=#ff0000], the figure is called a polygon. [br]The line segments that make up a polygon become its sides. [br] The endpoints of the line segments are [/color][color=#0000ff][url=https://www.mathopenref.com/vertex.html]vertices[/url][/color][color=#ff0000] of the polygon. [br]The (interior) angles of a polygon are the angles formed by two adjacent sides. [br][/color][/b][/size][/size]
Non-Example
Not a Polygon. The figure is closed, but the closed curve is not made up entirely of line segments.
Non-Example
Not a Polygon. The figure is made up entirely of line segments, but the figure is not closed.
Example
Polygon: The figure is closed and made up entirely of line segments.
[size=200][b][color=#ff0000]The polygon with the fewest number of sides is a TRIANGLE, which has three sides. [/color][/b][/size]
Triangle
A triangle is a polygon with the fewest number of sides.
[size=200][b][color=#0000ff]A triangle has three angles and therefore has three vertices[/color][/b][/size]
Naming the vertices and sides of a triangle
A triangle is a polygon with the fewest number of sides.
[b][color=#0000ff][size=150]When we label the vertices of a triangle with capital letters (ABC), the same lower case letters (abc) refer to the sides opposite the angle. [/size][/color][/b]
– Judith Hilinski

1.2.

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1.3.

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2.

Triangles Proofs and Theorems

Commit to memory

  • 1. Copy of triangle angle-sum theorem
  • 2. Triangle Sum Theorem

2.1.

Copy of triangle angle-sum theorem

– Judith Hilinski, sonom

2.2.

–

3.

Practice Problems

Guided Practice Solving Problems involving Triangles

  • 1. Practice Problems with Triangles

3.1.

Practice Problems with Triangles

Graphic 1
[b][color=#351c75][size=150]Study the image in Graphic 1. You should see two triangles. The vertices in each triangle are labeled with a capital letter. (A, B, C or D).[br][/size][/color][/b][size=150][b][color=#351c75]Use Graphic 1 to answer the first two questions. [/color][/b][/size]
[b][color=#134f5c][size=150]Which of the names below would not be correct when referring to triangle BDC?[/size][/color][/b]
[b][size=150][color=#274e13]Which "leg" or side segment do triangle ABC and triangle BDC share?[/color][/size][/b]
Graphic 2
[size=150][b][color=#0000ff]Study the image in Graphic 2. You should see a triangle with its vertices labeled A, B and C. [/color][/b][/size]
[size=150][b][color=#134f5c]In triangle ABC, what is the side opposite the vertex labeled A?[/color][/b][/size]
[size=150][b][color=#0b5394]In triangle ABC, what is the angle opposite the side labeled b?[/color][/b][/size]
[size=150][b][color=#134f5c]Which of the following is true about the angle labeled C in triangle ABC?[/color][/b][/size]
[size=150][b][color=#0b5394]How might we classify triangle ABC?[/color][/b][/size]
[b][size=200][color=#ff0000]Closed Curve, Polygon, Triangle[br][size=100][size=150]For each figure, determine if it classified as a closed curve, polygon, triangle, or none of the above. Each may have more than one answ[/size][/size][size=150]er.[/size][br][/color][/size][/b]
How could the figure above be classified?
How could the figure above be classified?
How could the figure above be classified?
How could the figure above be classified?
How could the figure above be classified?
– Judith Hilinski

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