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
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Definition |
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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:
Angle a must be 180-34-116=30, since angle b is par tof a straight angle, its measure is 180-116=64. Finaly angle c is found, 180-64-67=49.
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 images, except where otherwise noted, adapted from “MATH 1420: Geometry Concepts for Teachers” by the RSCC Math 1410/1420 OER Team under Creative Commons Attributions 4.0 International License.
- Images from Wikimedia Commons
- Warning Sign, Alexandru Panoiu from Bucharest, Romania, Wikimedia Commons, CC BY 2.0
- Flag of Mughal Empire, Gryffindor, Wikimedia Commons, CC0.
- Dual square radial elongated triangular tiling, Tomruen, Wikimedia Commons, CC BY-SA 4.0
- Braunton (Devon, UK), Countryside Centre — 2013 — 00192, Dietmar Rabich, Wikimedia Commons, CC BY-SA 4.0
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