Download Classifying triangles

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.

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 the
screen. 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
happen
this can never
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
FALSE

“A right triangle can NEVER be
equilateral since the hypotenuse is
always longer than the other two sides”

“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

equiangular
regular
obtuse
acute
•
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 2012
< http://www.cliffsnotes.com/study_guide/topicArticleId-18851,articleId18785.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/classifyingtriangles/classifying-triangles.html
http://www.factmonster.com/math/know
ledgebox/
http://www.uff.br/cdme/jct/jct-html/jcten.html