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