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Unit 2

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Triangles

Definition of Triangle

A geometric figure formed by three segments joining noncollinear points .

B

C

A

Naming Triangles

Triangles are named by using its vertices.

For example, we can call the following triangle:

∆ABC

∆ACB

∆BAC

∆BCA

∆CAB

∆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

Equilateral:

A

A

B

C

C

BC

=

3.55

cm

B

BC

=

5.16

cm

G

H

I

HI

=

3.70

cm

Scalene:

A triangle in which all 3 sides are different lengths.

AC = 3.47 cm

AB = 3.47 cm

AB = 3.02 cm

AC = 3.15 cm

Isosceles:

A triangle in which at least 2 sides are equal.

- A triangle in which all 3 sides are equal.

GI = 3.70 cm

GH = 3.70 cm

A triangle in which all 3 angles are less than 90˚.

G

°

76

°

°

57

47

H

I

A

°

44

°

108

°

28

C

B

Acute:

Obtuse:

- A triangle in which one and only one angle is greater than 90˚& less than 180˚

Right:

- A triangle in which one and only one angle is 90˚

Equiangular:

- A triangle in which all 3 angles are the same measure.

polygons

triangles

scalene

isosceles

equilateral

Classification by Sides

with Flow Charts & Venn Diagrams

Polygon

Triangle

Scalene

Isosceles

Equilateral

Lesson 3-1: Triangle Fundamentals

polygons

triangles

right

acute

equiangular

obtuse

Classification by Angles

with Flow Charts & Venn Diagrams

Polygon

Triangle

Right

Obtuse

Acute

Equiangular

Helpful Triangle Information

Triangle Sum:

The sum of the interior angles in a triangle is 180˚.

Third Angle of a Triangle:

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

Fact # 1:

Each angle in an equiangular triangle is 60˚.

Fact # 2:

Acute angles in a right triangle are complementary.

There can be at most one right or obtuse angle in a triangle.

Fact # 3:

Exterior Angle and Remote Interior Angles

Exterior Angle -

An angle formed by one side of a triangle and the extension of another side of the triangle.

Remote Interior Angles –

Interior angles that are not adjacent to the exterior angle of the triangle.

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

Example:

Find the mA.

B

C

3x - 22 = x + 80

3x – x = 80 + 22

2x = 102

mA = x = 51°