Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle:...

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Transcript of Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle:...

Page 1: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 1

Triangle Fundamentals

Page 2: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 2

Naming Triangles

For example, we can call the following triangle:

Triangles are named by using its vertices.

∆ABC ∆BAC

∆CAB ∆CBA∆BCA

∆ACB

A

B

C

Page 3: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle 4

Classifying Triangles by Sides

Equilateral:

Scalene: A triangle in which all 3 sides are different lengths.

Isosceles: A triangle in which at least 2 sides are equal.

A triangle in which all 3 sides are equal.

AB

= 3

.02

cm

AC

= 3.15 cm

BC = 3.55 cm

A

B CAB =

3.47

cmAC = 3.47 cm

BC = 5.16 cmBC

A

HI = 3.70 cm

G

H I

GH = 3.70 cm

GI = 3.70 cm

Page 4: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 5

Classifying Triangles by Angles

Acute:

Obtuse:

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

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

108

44

28 B

C

A

57 47

76

G

H I

Page 5: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Lesson 3-1: Triangle Fundamentals

6

Classifying Triangles by Angles

Right:

Equiangular:

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

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

34

56

90B C

A

60

6060C

B

A

Page 6: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 7

polygons

Classification by Sides with Flow Charts & Venn Diagrams

triangles

Scalene

Equilateral

Isosceles

Triangle

Polygon

scalene

isosceles

equilateral

Page 7: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 8

polygons

Classification by Angles with Flow Charts & Venn Diagrams

triangles

Right

Equiangular

Acute

Triangle

Polygon

right

acute

equiangular

Obtuse

obtuse

Page 8: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 9

Theorems

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

Triangle Sum Theorem:

B

A C

32

1

Page 9: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 10

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.

Exterior AngleRemote Interior Angles A

BC

D

m ACD m A m B

Page 10: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 11

Exterior Angle Theorem

Given: Triangle ABC with Exterior angle ACDProve:

A

BC

D

m ACD m A m B

Page 11: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Triangle Fundamentals 12

Exterior Angle Theorem

Example:

(3x-22)x80

B

A DC

Find the mA.

3x - 22 = x + 80

3x – x = 80 + 22

2x = 102

mA = x = 51°

Page 12: Triangle Fundamentals 1. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB.

Homework

HW pg 221 # 1 to 6, 17, 18, 19 pg 222 #32 to 37

Triangle Fundamentals 13


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