Skip to main content
UploadLanguage (EN)Support
BusinessMobileSocial MediaMarketingTechnologyArt & PhotosCareerDesignEducationPresentations & Public SpeakingGovernment & NonprofitHealthcareInternetLawLeadership & ManagementAutomotiveEngineeringSoftwareRecruiting & HRRetailSalesServicesScienceSmall Business & EntrepreneurshipFoodEnvironmentEconomy & FinanceData & AnalyticsInvestor RelationsSportsSpiritualNews & PoliticsTravelSelf ImprovementReal EstateEntertainment & HumorHealth & MedicineDevices & HardwareLifestyle
Uploaded bysmiller5
367 views

6.2 Classifying Triangles

Triangles can be classified based on their side lengths and angle measures. There are three types based on sides - equilateral (all sides equal), isosceles (two or more equal sides), and scalene (no equal sides). There are also four types based on angles - acute (all angles less than 90 degrees), right (one 90 degree angle), obtuse (one angle greater than 90 degrees), and equiangular (all angles equal). The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. This can be used to determine if a set of side lengths forms a triangle or the possible range of values for the third side.

Education◦
Download to read offline
Classifying Triangles The student is able to (I can): • Classify triangles by angles and by sides • Analyze the relationship between the angles of a triangle and the lengths of the sides • Determine allowable lengths for sides of triangles
Classifying Triangles Triangles are classified by their side lengths and their angle measures as follows: • By side length – equilateral – all sides congruent (equal) – isosceles – two or moreor moreor moreor more sides congruent – scalene – no sides congruent • By angle measure – acute – all acute angles – right – one right angle – obtuse – one obtuse angle – equiangular – all angles congruent
Practice Classify each triangle by its angles and sides. 1. 3. 2. 4. 90° 110°
Practice Classify each triangle by its angles and sides. 1. 3. 2. 4. 90° 110° right scalene equiangular equilateral acute isosceles obtuse isosceles
If two sides of a triangle are not congruent, then the larger angle is opposite the longer side. If two angles of a triangle are not congruent, then the longer side is opposite the larger angle. A C T AT > AC → m∠C > m∠T m∠C > m∠T → AT > AC
Example: Given the side lengths, put the angles in order from smallest to largest. ∠P is across from 16, ∠N is across from 19, and ∠A is across from 31, so it would be: ∠P, ∠N, and ∠A P A N 19 31 16
Example: Given the angle measures, put the side lengths in order from smallest to largest. First, we have to calculate m∠E: m∠E = 180- (70+30) = 80° So the sides would be: TE < EN < TN T E N 70° 30°
Triangle Inequality Theorem The sum of any two side lengths of a triangle is greater than the third side length. Example: 1. Which set of lengths forms a triangle? 4, 5, 10 7, 9, 12 4 + 5 < 10 7 + 9 > 12
Note: To find a range of possible third sides given two sides, subtract for the lower bound and add for the upper bound. Examples: 2. What is a possible third side for a triangle with sides 8 and 14? 14 – 8 = 6 lower bound 14 + 8 = 22 upper bound The third side can be between 6 and 22.
3. What is the range of values for the third side of a triangle with sides 11 and 19? 19 – 11 = 8 lower bound 19 + 11 = 30 upper bound 8 < x < 30