Geometry

1
Geometry

• Notes Section 4-1

2
What youll 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.

3
Vocabulary

• Sides of a triangle
• Vertices of a triangle
• Acute triangle
• Obtuse triangle
• Right triangle
• Equiangular triangle
• Scalene triangle
• Isosceles triangle
• Equilateral triangle

4
The parts of a triangle

• 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

The vertices of this triangle are
F,
S,
and H
5
The parts of a triangle

• The sides are line segments
• Segments are named by endpoints
• Sides will have measure (like inches)

The sides of this triangle are
FS,
SH,
and HF
6
The parts of a triangle

• Every triangle will have three angles
• Angles are named by ? with three points (vertex
  in middle) , ? with just the vertex, or ?
  with a number

The angles of this triangle are
?F or ?SFH,
?S or ?FSH,
and ?H or ?SHF
7
NAMING A TRIANGLE

• Triangles are named by their vertices

C
THIS TRIANGLE CAN BE CALLED
?ACT
?TAC
A
T
?CAT
You must include the ? symbol
8
Classifying Triangles by Angles

• Acute Trianglestriangles with all 3 angles
  measuring less than 90
• Obtuse trianglestriangles with exactly ONE angle
  measuring between 90 and 180
• Right Triangles triangles with exactly ONE right
  angle (marked with a box)
• Equiangular Trianglestriangle with all angles
  exactly the same measure (all are congruent to
  each other)

9
Classifying Triangles by Sides

• Scalene Trianglestriangles with no 3 sides of
  equal measure (no congruent sides)
• Isosceles trianglestriangles with at least TWO
  sides of equal measure (2 congruent sides)
• Equilateral Trianglestriangle with all sides
  exactly the same measure (all 3 sides congruent
  to each other)

10
Parts of an Isosceles Triangle
Vertex angle
Vertex angle
Vertex angle

• The vertex angle is always the angle between the
  two congruent sides the other angles are called
  base angles.

11
Example Problem 1

• Find x if ?JMN is isosceles with JM MN.

M
2x 5
3x 9
N
J
x - 2
12
Example Problem 2

• ?FGH is equilateral. With FG x 5, GH 3x
  9, and FH 2x - 2 . Find x and the length of
  each side

G
x 5
3x 9
H
F
2x - 2
13
Example Problem 3

• Classify ?RST by its sides.

S(2, 5)
T(4, 2)
R(0, 2)
S
T
R
14
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?

• Assignment
• NON-PROOFWorksheet 4-1
• PROOF P. 181(22-44E, 50-56E)