8 Triangles
Learning Objectives
Objectives:
- Determine the types of triangle
- Find the measure of unknown angles of a triangle
- Use the Pythagorean Theorem
Types of Triangles
Definition |
Illustration |
Example |
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A triangle containing one right angle is a right triangle. The [latex]\right[/latex] symbol in one angle indicates that the angle is a right angle.
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A triangle in which all the angles are acute is an acute triangle. |
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A triangle containing one obtuse angle is an obtuse triangle. |
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A triangle with no congruent sides is a scalene triangle. |
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A triangle with at least two congruent sides is an isosceles triangle. |
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A triangle with all sides congruent is an equilateral triangle. |
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The Sum of the Angles of a Triangle
The angles measures of a triangle sum to 180 degrees.
Examples
Find the unknown angle(s) in the given figures.
Solution: 
Solution:
Side Lengths in a Right Triangle
The Pythagorean Theorem gives the relationship between the sides of a right triangle.
Examples
Find the unknown side of the given triangles. Round your answer to two decimal places as necessary.
Solution:
2.
Solution:
3.
A painter places a 20-foot ladder against the side of a house. The base of the ladder is 5 feet from the side of the house. How far up the house is the top of the ladder?
Solution:
Let a be the side of the house. Thus
Attributions
- Content and structure adapted from RSCC Math 1410/1420 OER Team, 2022, CC BY 4.0.
- Triangle example pictures from Wiki Commons
- https://commons.wikimedia.org/wiki/File:Warning_Sign_%22Children%22_in_Constan%C8%9Ba_(AP4L2897_1PSP)_(20620522889).jpg
- https://commons.wikimedia.org/wiki/File:Flag_of_the_Mughal_Empire.png
- https://commons.wikimedia.org/wiki/File:Dual_square_radial_elongated_triangular_tiling.svg
- https://commons.wikimedia.org/wiki/File:Braunton_(Devon,_UK),_Countryside_Centre_–_2013_–_00192.jpg
- https://commons.wikimedia.org/wiki/File:Triangle-50-60-70.svg
