Classifying trianglesBy: Sarah Smith

introduction

Subject: Mathematics-GeometryGrade-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.

Definition of a triangle

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

2 ways to classify triangles

By sides: 3 types› Equilateral› Scalene› Isosceles

By angles: 4 types› Right› Acute› Obtuse› Equiangular

Click on each image to learn more about it then proceed to the quiz questions

Equiangular

*This is the screen. Return here after each triangle.

Click here for QUIZ

EQ

UILA

TER

AL

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 °

SC

ALE

NE

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

ISO

SC

ELE

S

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.

EQ

UIA

NG

ULA

R

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

AC

UTE

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

OB

TU

SE

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

RIG

HT

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

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

3

21

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

TRUE FALSE

CORRECT!

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

WRONG! (sorry)

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

2) Classify this triangle by angle measure

A.B.

C.

D.

isosceles

acute

scalene

equiangular

CORRECT!

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

WRONG! (sorry)

Isosceles is a classification based on side length, not angle

WRONG! (sorry)

Scalene is a classification based on side length not angle.

WRONG! (sorry)

Equiangular means all 3 angles are congruent

This triangle only had 2 angles that were congruent

3) If a triangle is equilateral it cannot also be:

A.B.C.D.

acute

regular

equiangular

obtuse

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°

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”

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”

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

I hop

e y

ou

learn

ed

som

eth

ing

. Next tim

e

we w

ill learn

how

to u

se th

e P

yth

ag

ore

an

Th

eore

m

Refe

rence

sA

dditio

nal Fu

n Lin

ks

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