Loading...

PPT – Triangle Fundamentals PowerPoint presentation | free to download - id: 6c2b61-MmVhN

The Adobe Flash plugin is needed to view this content

Lesson 3-1

- Triangle Fundamentals

Naming Triangles

Triangles are named by using its vertices.

For example, we can call the following triangle

?ABC

?BAC

?ACB

?CAB

?BCA

?CBA

Opposite Sides and Angles

Opposite Sides

Side opposite to ?A

Side opposite to ?B

Side opposite to ?C

Opposite Angles

Angle opposite to ?A

Angle opposite to ?B

Angle opposite to ?C

Classifying Triangles by Sides

Scalene

A triangle in which all 3 sides are different

lengths.

AB 3.47 cm

AC 3.47 cm

AB 3.02 cm

AC 3.15 cm

Isosceles

A triangle in which at least 2 sides are equal.

- Equilateral

A triangle in which all 3 sides are equal.

GI 3.70 cm

GH 3.70 cm

Classifying Triangles by Angles

Acute

- A triangle in which all 3 angles are less than

90.

Obtuse

A triangle in which one and only one angle is

greater than 90 less than 180

Classifying Triangles by Angles

Right

A triangle in which one and only one angle is 90

Equiangular

A triangle in which all 3 angles are the same

measure.

Classification by Sides with Flow Charts Venn

Diagrams

Polygon

Triangle

Scalene

Isosceles

Equilateral

Classification by Angles with Flow Charts Venn

Diagrams

Polygon

Triangle

Right

Acute

Obtuse

Equiangular

Theorems Corollaries

The sum of the interior angles in a triangle is

180.

Triangle Sum Theorem

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.

Corollary 1

Each angle in an equiangular triangle is 60.

Corollary 2

Acute angles in a right triangle are

complementary.

There can be at most one right or obtuse angle in

a triangle.

Corollary 3

Exterior Angle Theorem

The measure of the exterior angle of a triangle

is equal to the sum of the measures of the remote

interior angles.

Remote Interior Angles

A

Exterior Angle

D

B

Example

Find the m?A.

C

3x - 22 x 80 3x x 80 22 2x 102

m?A x 51

Median - Special Segment of Triangle

Definition

A segment from the vertex of the triangle to the

midpoint of the opposite side.

Since there are three vertices, there are three

medians.

In the figure C, E and F are the midpoints of the

sides of the triangle.

Altitude - Special Segment of Triangle

The perpendicular segment from a vertex of the

triangle to the segment that contains the

opposite side.

Definition

In a right triangle, two of the altitudes of are

the legs of the triangle.

In an obtuse triangle, two of the altitudes are

outside of the triangle.

Perpendicular Bisector Special Segment of a

triangle

A line (or ray or segment) that is perpendicular

to a segment at its midpoint.

Definition

The perpendicular bisector does not have to start

from a vertex!

Example

A

E

A

B

In the isosceles ?POQ, is the

perpendicular bisector.

B

In the scalene ?CDE, is the

perpendicular bisector.

In the right ?MLN, is the perpendicular

bisector.