Lesson:
Objectives:
4.1 Classifying Triangles
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 Some DEFINITIONS
POLYGON –
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 Equilateral 3 sides Equiangular 3 Angles
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:
Pages:
Objectives:
4.2 Measuring Angles in Triangles
189 – 192
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
605 2
135 1 3 4
GEOMETRY 4.2
Definition: COROLLARY
A statement that can be easily proved using a theoremis 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