Transcript Document 7114979

Geometry
Notes Section 4-1
What you’ll learn. . . .
How to identify and name the
parts of a triangle.
 How to identify and classify
triangles by angles.
 How to identify and classify
triangles by sides.
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Vocabulary
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Sides of a triangle
Vertices of a triangle
Acute triangle
Obtuse triangle
Right triangle
Equiangular triangle
Scalene triangle
Isosceles triangle
Equilateral triangle
The parts of a triangle
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The vertices of a triangle are the corner points
joining the sides of the triangle
 Points are named with capital printed letters
 One corner is called a VERTEX more than
one, VERTICES
S
The vertices of this triangle
are:
F,
F
H
S,
and H
The parts of a triangle
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The sides are line segments
 Segments are named by endpoints
 Sides will have measure (like inches)
S
The sides of this triangle are:
FS,
F
H
SH,
and HF
The parts of a triangle
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Every triangle will have three angles
 Angles are named by “” with three points
(vertex in middle) , “” with just the vertex, or
“” with a number
S
The angles of this triangle
are:
F or SFH,
S or FSH,
F
H
and H or SHF
NAMING A TRIANGLE
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Triangles are named by their vertices
C
THIS TRIANGLE
CAN BE CALLED
ΔACT
A
T
ΔTAC
ΔCAT
You must include the Δ symbol
Classifying Triangles by Angles
Acute Triangles—triangles with all 3
angles measuring less than 90°
 Obtuse triangles—triangles with exactly
ONE angle measuring between 90° and
180°
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Right Triangles– triangles with exactly ONE
right angle (marked with a box)
Equiangular Triangles—triangle with all angles
exactly the same measure (all are congruent to
each other)
Classifying Triangles by Sides
Scalene Triangles—triangles with no 3
sides of equal measure (no congruent
sides)
 Isosceles triangles—triangles with at least
TWO sides of equal measure (2 congruent
sides)
 Equilateral Triangles—triangle with all
sides exactly the same measure (all 3
sides congruent to each other)
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Parts of an Isosceles Triangle
Vertex
angle
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Vertex
angle
Vertex
angle
The vertex angle is always the angle
between the two congruent sides; the
other angles are called base angles.
Example Problem #1:
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Find x if ΔJMN is isosceles with JM =
MN.
M
2x – 5
J
3x – 9
x-2
N
Example Problem #2:
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ΔFGH is equilateral. With FG = x + 5, GH = 3x – 9,
and FH = 2x - 2 . Find x and the length of each
side
G
3x – 9
x+5
F
2x - 2
H
Example Problem #3:
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Classify ΔRST by its sides.
R(0, 2)
S
R
T
S(2, 5)
T(4, 2)
Have you learned. . . .
How to identify and name the
parts of a triangle?
 How to identify and classify
triangles by angles?
 How to identify and classify
triangles by sides?
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Assignment:
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NON-PROOF:Worksheet 4-1
PROOF: P. 181(22-44E, 50-56E)