Download 4.1ClassifyingTriangles

Journal Warm Up
Dec. 21, 2009
List as many types of triangles as
you can think of!
4.1 Classifying Triangles
Triangle
Figure formed by 3 segments
joining 3 points.
Vertex
Point joining two sides of a
triangle.
4.1 Classifying Triangles
Legs
On a right triangle: sides which
form the right angle.
On an isosceles triangle: sides
which are congruent.
Hypotenuse
The longest side on a triangle.
Base
The non-congruent side in an
isosceles triangle.
4.1 Classifying Triangles
Adjacent Sides Two sides sharing a common
vertex.
4.1 Classifying by Sides
Equilateral
Triangles with 3 congruent sides.
Isosceles
Triangle with at least 2 congruent
sides.
Scalene
Triangle with no congruent sides.
4.1 Classifying by Angles
Acute
Triangle with 3 acute angles.
Equiangular
Triangles with 3 congruent angles.
Right
Triangle with one right angle.
Obtuse
Triangle with one obtuse angle.
Sort the last seven terms into two
categories:
Classifying By Sides
Classifying By Angles
Try it!
• Classifying Triangles (by sides & by
angles) with your NEIGHBOR.
• Note that each triangle will have AT
LEAST 2 answers.
Closer
• Journal: Why can’t an obtuse triangle have
more than one obtuse angle?
Warm Up
Dec. 22, 2008
• Journal: Classify the triangle by angle and
by sides.
60º
60º
Goals Today
• Discuss Classification of Triangles
• Define Triangle Theorems
• Apply Triangle Theorems
4.1 More Vocabulary
Interior Angles
Angles which are within
the triangle.
Angles formed when
triangle sides are
extended.
Exterior Angles
1
2
3
4
4.1 Theorems
Triangle Sum
The sum of the interior
Theorem (Thm. 4.1) angles in a triangle is
180º.
The measure of an
Exterior Angle
Theorem (Thm. 4.2) exterior angle equals
the sum of the two nonadjacent interior angles.
The acute angles of a right
Corollary to Thm. 4.2
triangle are
complimentary.
Example 1: Classifying Triangles
a) By sides:
By angles:
20º L
23
J
50º
19
110º
K
Example 2: Classifying Triangles
b) By sides:
By angles:
Z
45º
4
X
5.7
45º
Y
Example 2: Finding Angle
Measures
a) Find the value of x.
(4x-5)º
(3x+11)º
Example 2: Finding Angle
Measures
b) Find the value of y.
2yº
50º
On your own: Exercises.
• # 1-5 all. Ask for help if you need it!
With a Neighbor…
• 4.1 Practice A
Closer
• Homework: “Interior and Exterior Angles”
• Journal: When would you have an acute
exterior angle?
Warm Up
Dec. 23, 2009
• Homework Check (Interior and Exterior
Angles)
• Journal: Find the value of x.
3xº
30º
2xº
In Congruent Triangles,
Order Matters
• ΔABC = ΔDEF
D
A
E
B
C
F
Goals Today
• Corresponding Triangle Parts
• http://www.youtube.com/watch?v=fks_6d1
prC8&feature=fvw
Closer
• Journal: Fill in the missing angles:
60º
50º
?
30º
?
?