CK12 - Trigonometry

(e.g, like the handsof a clock.)Giventhe importantof anglesin the studyof trigonometry, in this lessonwe
will reviewsomeimportantaspectsof trianglesand their angles.We’ll beginby categorizingdifferentkinds
of triangles.

Trianglesand theirinteriorangles

Formally, a triangleis definedas a 3-sidedpolygon.This meansthat a trianglehas 3 sides,all of whichare
(straight)line segments.We can categorizetriangleseitherby their sides,or by their angles.The tablebelow
summarizesthe differenttypesof triangles.

Name Description Note

A trianglewith threeequal sidesand 3This type of triangleis acute.

congruentangles

Equilateral/equi-angular

A trianglewith 2 equalsidesand two equalAn equilateraltriangleis also isosceles.

angles

Isosceles

Scalene A trianglewith no pairsof equalsides

It is not possiblefor a triangleto havemore

than one 90oangle(see below.)

Right A trianglewith one 90oangle

A trianglein whichall 3 anglesmeasure

less than 90o

Acute

It is not possiblefor a triangleto havemore

than one obtuseangle(see below.)

A trianglein whichone angleis greater

than 90

o

Obtuse

In the followingexample,we will categorizespecifictriangles.

Example1:Determinewhichcategorybest describesthe triangle:

a. A trianglewith side lengths3, 7, and 8

b. A trianglewith side lengths5, 5, and 5

c. A trianglewith side lengths3, 4, and 5

Solution:

a. This is a scalenetriangle.