Download Classifying Triangles

4.1 Notes
Classifying Triangles
You can classify triangles by their angle measures or by their sides
Angle Measures
(You use angle measures to classify
Triangles)
Equiangular Triangle:
A triangle with three congruent angles.
Side Measures
(You use side measures to classify Triangles)
Equilateral Triangle:
A triangle with three congruent sides.
X
Y
Z
̅̅̅̅
Acute Triangle
All Angles in the triangle are acute angles.
All angles are between 0˚ & 90˚. (An
Equiangular Triangle is also an Acute
Triangle).
B
̅̅̅̅
̅̅̅̅
Isosceles Triangle
At least two sides of the triangle are
congruent. (An equilateral triangle is also
an isosceles triangle).
X
30˚
Y
70˚
A
Z
̅̅̅̅
80˚
T
̅̅̅̅
Classifying Triangles: (continued)
You can classify triangles by their angle measures or by their sides
Obtuse Triangle
There is one obtuse angle in the triangle.
Largest side is across from largest angle.
Smallest side is across from the smallest
angle.
G
Scalene Triangle
No sides are congruent. No angles are
congruent.
Smallest angle is across from the smallest
side and the Largest angle is across from
the largest side.
D
R
K
M
Q
Right Triangle
There is one right angle in the triangle.
Pythagorean Theorem, special right
formulas and SOHCAHTOA is used with
Right Triangles. You must remember that
the hypotenuse is ALWAYS the largest side
and always across from the right angle.
The legs always make the right angle.
W
Leg
Hypotenuse
K
Leg
Z
Knowing how to classify a triangle helps us to find angle measures or side measures
when an algebraic expression has been attached to the angle or the side, or finding
angles or sides to classifying triangles.
a. You can use angle measures to classify
∠JLM and ∠JLK form a linear pair,
so they are supplementary (must add to 180˚).
Using angle addition we know m ∠JLM + m ∠JLK = 180
m∠JLM + 120 = 180
m∠JLM = 60˚
Definition of Supplementary angles
Substitution Property
Subtraction Property of Equality
Since all the angles in
are congruent,
is an equiangular triangle.
b. You can use triangle classification to find the side lengths of a triangle
You only need two sides to make an equation. Even though this is equilateral, we only
need two sides to solve for x, then plug it in to find the length of all three sides.
̅̅̅̅
̅̅̅̅
4x = 3x + 5
x =5
Definition of Congruent Segments
Substitution Property of Equality
Subtraction Property of Equality
Substitute 5 back into 4x and 3x +5 and you will see both sides 4(5) = 3(5) +5 = 20.
Because this is an equilateral Triangle by the tick marks, you know all three sides equal
30 units.