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Classifying triangles

Classifying triangles. By: Sarah Smith. introduction. Subject: Mathematics-Geometry Grade-level: Sophomore (10 th grade) Educational Objective: Be able to identify and classify triangles by angles and/or sides Instructions:

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Classifying triangles

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  1. Classifying triangles By: Sarah Smith

  2. introduction Subject: Mathematics-Geometry Grade-level: Sophomore (10th grade) Educational Objective: Be able to identify and classify triangles by angles and/or sides Instructions: Progress through the educational slides and then complete the three short quiz questions by clicking on the corresponding letter or word.

  3. Definition of a triangle • A closed figure consisting of three line segments linked end-to-end

  4. 2 ways to classify triangles • By sides: 3 types • Equilateral • Scalene • Isosceles • By angles: 4 types • Right • Acute • Obtuse • Equiangular

  5. Click on each image to learn more about it then proceed to the quiz questions Equiangular Click here for QUIZ *This is the screen. Return here after each triangle.

  6. Equilateral 3 sides equal length Because all three sides are congruent, all three interior angles are also, making it the same as an equiangular triangle It is possible to construct using a ruler and a compass All three interior angles =60 °

  7. Scalene 0 sides equal length Interior angles all have different measures The shortest side if opposite the smallest angle The longest side is opposite the largest angle

  8. Isosceles 2 sides equal length The unequal side of an isosceles triangle is usually referred to as the 'base' of the triangle. The base angles of an isosceles triangle are always equal. The altitude is a perpendicular distance from the base to the topmost vertex.

  9. equiangular 3 angles equal measures All three sides of an equiangular triangle are congruent (same length). For an equiangular triangle, the radius of the incircle is exactly half the radius of the circumcircle. Also classified as an equilateral triangle

  10. Acute All 3 angles less than 90 ° In any triangle, two of the interior angles are always acute (less than 90 °) *so there are three possibilities for the third angle: Less than 90° - all three angles are acute and so the triangle is acute. Exactly 90° - it is a right triangle Greater than 90° (obtuse): the triangle is an obtuse triangle

  11. Obtuse 1 angle greater than 90 ° The internal angles of any triangle always add up to 180°. If two angles were greater than 90° they would add to more then 180° just by themselves. Therefore this can never happen

  12. Right 1 angle measures 90 ° A right triangle can NEVER be equilateral since the hypotenuse is always longer than the other two sides Trigonometry concerns itself almost exclusively with the properties of right triangles The Pythagorean Theorem defines the relationship between the 3 sides of a right triangle A^2+B^2=C^2

  13. QUIZ TIME Click on each number in order to answer the following quiz questions. 2 1 3

  14. 1) A right triangle can be equilateral if all three side are the same length. • TRUE • FALSE

  15. CORRECT! • “A right triangle can NEVER be equilateral since the hypotenuse is always longer than the other two sides”

  16. WRONG! (sorry) • “A right triangle can NEVER be equilateral since the hypotenuse is always longer than the other two sides”

  17. 2) Classify this triangle by angle measure A. isosceles B. acute C. scalene D. equiangular

  18. CORRECT! • Acute is a classification based on angle • All 3 angles less than 90 °

  19. WRONG! (sorry) • Isosceles is a classification based on side length, not angle

  20. WRONG! (sorry) • Scalene is a classification based on side length not angle.

  21. WRONG! (sorry) • Equiangular means all 3 angles are congruent • This triangle only had 2 angles that were congruent

  22. 3) If a triangle is equilateral it cannot also be: A. equiangular B. regular C. obtuse D. acute

  23. CORRECT! • The internal angles of any triangle always add up to 180°. If two angles were greater than 90° they would add to more then 180° just by themselves. • Therefore this can never happen because obtuse means 1 angles greater than 90°

  24. WRONG! (sorry) • Definition of equilateral: • “Because all three sides are congruent, all three interior angles are also, making it the same as an equiangular triangle”

  25. WRONG! (sorry) • A regular polygon is one that has all congruent side lengths and all congruent angle measures • Therefore making and equiangular, equilateral triangle a “regular triangle”

  26. WRONG! (sorry) • “The internal angles of any triangle always add up to 180°. If two angles were greater than 90° they would add to more then 180° just by themselves.” • If all three angles are less than 90° then it and an acute triangle

  27. I hope you learned something. Next time we will learn how to use the Pythagorean Theorem References • CliffsNotes.com. Classifying Triangles by Sides or Angles. 19 Jul 2012< http://www.cliffsnotes.com/study_guide/topicArticleId-18851,articleId- 18785.html>. • Math Open Reference. (2009). Classifying triangles. Retrieved from http://www.mathopenref.com/triangleclassify.html • CCSSI. (2012). Common core state standards. Retrieved from http://www.corestandards.org/the-standards/mathematics • Ohio Department of Education. (2012, August 01). Mathematics model curriculum. Retrieved from http://www.education.ohio.gov/GD/Templates/Pages/ ODE/ODEDetail.aspx?page=3&TopicRelationID=1696&ContentID=126041& Content=127896 • http://www.math-play.com/classifying-triangles/classifying-triangles.html • http://www.factmonster.com/math/knowledgebox/ • http://www.uff.br/cdme/jct/jct-html/jct-en.html Additional Fun Links

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