Subject: Mathematics-Geometry Grade-level: Sophomore (10 th 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.

 A closed figure consisting of three line segments linked end-to-end

 By sides: 3 types › Equilateral › Scalene › Isosceles  By angles: 4 types › Right › Acute › Obtuse › Equiangular

Equiangular *This is thescreen. Return here after each triangle. Click here for QUIZ

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 °

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

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.

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

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

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

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

Click on each number in order to answer the following quiz questions.

 TRUE TRUE  FALSE FALSE

 “A right triangle can NEVER be equilateral since the hypotenuse is always longer than the other two sides”

isosceles acute scalene equiangular

 Acute is a classification based on angle  All 3 angles less than 90 °

 Isosceles is a classification based on side length, not angle

 Scalene is a classification based on side length not angle.

 Equiangular means all 3 angles are congruent  This triangle only had 2 angles that were congruent

acute regular equiangular obtuse

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°

 Definition of equilateral: › “Because all three sides are congruent, all three interior angles are also, making it the same as an equiangular triangle”

 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”

 “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

References Additional Fun Links  CliffsNotes.com. Classifying Triangles by Sides or Angles. 19 Jul  Math Open Reference. (2009). Classifying triangles. Retrieved from  CCSSI. (2012). Common core state standards. Retrieved from  Ohio Department of Education. (2012, August 01). Mathematics model curriculum. Retrieved from ODE/ODEDetail.aspx?page=3&TopicRelationID=1696&ContentID=126041& Content=  triangles/classifying-triangles.html triangles/classifying-triangles.html  ledgebox/ ledgebox/  en.html en.html