Download Geometry 4.1 Some DEFINITIONS POLYGON

Lesson: 4.1 Classifying Triangles
Objectives:
 To IDENTIFY parts of triangles
 To CLASSIFY Triangles by their Parts
Geometry 4.1
Some DEFINITIONS
• acute triangle
• obtuse triangle
• right triangle
• equiangular triangle
• scalene triangle
• isosceles triangle
• equilateral triangle
Geometry 4.1
POLYGON –
Some DEFINITIONS
Geometry 4.1
Some DEFINITIONS
POLYGON –

a closed figure in a Plane
Geometry 4.1
Some DEFINITIONS
POLYGON –

a closed figure in a Plane
 made-up of Segments that
Geometry 4.1
Some DEFINITIONS
POLYGON –

a closed figure in a Plane
 made-up of Segments that
 intersect only at their Endpoints, called VERTICES.
Geometry 4.1
Some DEFINITIONS
POLYGON –

a closed figure in a Plane
 made-up of Segments that
 intersect only at their Endpoints, called VERTICES.
TRIANGLE –
 a three-sided Polygon
 consisting of Sides, Vertices, and Angles
Geometry 4.1
Geometry 4.1
Geometry 4.1
Geometry 4.1
Geometry 4.1
Geometry 4.1
Equiangular
Geometry 4.1
Equiangular
Parts of a Right Triangle
Geometry 4.1
Classification of Triangles
Angles
Acute
3 Acute Angles
Obtuse
1 Obtuse Angle
Right
1 Right Angle
Equiangular 3  Angles
Geometry 4.1
Geometry 4.1
Geometry 4.1
Geometry 4.1
Geometry 4.1
Geometry 4.1
Geometry 4.1
Classification of Triangles
Angles
Sides
Acute
3 Acute Angles Scalene
No 2 sides 
Obtuse
1 Obtuse Angle Isosceles
At Least 2 sides 
Right
1 Right Angle
Equiangular 3  Angles
Equilateral 3 sides 
Geometry 4.1
COORDINATE GEOMETRY Find the measures of the
sides of ΔRTS. Classify the triangle by sides.
Geometry 4.1
You should be able to:
 DEFINE a POLYGON
 DEFINE a TRIANGLE
 CLASSIFY a Triangle by Type of ANGLES
 CLASSIFY a Triangle by Type of SIDES
 NAME the Parts of a RIGHT Triangle
Lesson: 4.2 Measuring Angles in Triangles
Pages: 189 – 192
Objectives:
 To APPLY the ANGLE SUM Theorem
 To APPLY the EXTERIOR ANGLE Theorem
GEOMETRY 4.2
Slide 1 of 150
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
180 Theorem –
The SUM of the measures of the angles of a Triangle
is 180.
GEOMETRY 4.2
180 Theorem –
The SUM of the measures of the angles of a Triangle
is 180.
PROVE It!
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
THIRD ANGLE Theorem –
If TWO Angles of one Triangle are CONGRUENT to
TWO Angles of a second triangle,
then the THIRD angles of the triangles
ARE CONGRUENT.
GEOMETRY 4.2
THIRD ANGLE Theorem –
If TWO Angles of one Triangle are CONGRUENT to
TWO Angles of a second triangle,
then the THIRD angles of the triangles
ARE CONGRUENT.
GEOMETRY 4.2
THIRD ANGLE Theorem –
If TWO Angles of one Triangle are CONGRUENT to
TWO Angles of a second triangle,
then the THIRD angles of the triangles
ARE CONTRUENT.
PROVE It.
GEOMETRY 4.2
Definition: EXTERIOR ANGLE
An Exterior Angle is formed by one side of a triangle
and the extension of another side.
GEOMETRY 4.2
Definition: EXTERIOR ANGLE
An Exterior Angle is formed by one side of a triangle
and the extension of another side.
Definition: REMOTE INTERIOR ANGLES
The Interior Angles of the Triangle NOT adjacent
to a given Exterior Angle are Remote Interior Angles.
GEOMETRY 4.2
EXTERIOR ANGLE Theorem –
The measure of an EXTERIOR Angle of a Triangle
is EQUAL to
the SUM of the Measures
of the TWO REMOTE Interior Angles.
GEOMETRY 4.2
EXTERIOR ANGLE Theorem –
The measure of an EXTERIOR Angle of a Triangle
is EQUAL to
the SUM of the Measures
of the TWO REMOTE Interior Angles.
PROVE It.
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
5
135
1
2 60
3
4
GEOMETRY 4.2
Definition: COROLLARY
A statement that can be easily proved using a theorem
is called a COROLLARY.
1. The ACUTE ANGLES of a right triangle
are COMPLEMENTARY.
2. There can be at most one right or obtuse angle
in a triangle.
GEOMETRY 4.2
GEOMETRY 4.2
Solve for X in each Case.
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
You should be able to:
 PROVE the TOTAL DEGREES of INTERIOR ANGLES
of a Triangle
 DETERMINE the measure of the 3rd Angle of a Triangle
 Determine the EXTERIOR ANGLE from the 2 REMOTE
INTERIOR Angles
 STATE the Corollaries (1) Acute angles of a Right
Triangle (2) Number of Right/Obtuse Angles of a
Triangle
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
GEOMETRY 4.2
Geometry 4.1