Journal Warm UpDec. 21, 2009

List as many types of triangles as you can think of!

4.1 Classifying Triangles

Triangle

Vertex

Figure formed by 3 segments joining 3 points.

Point joining two sides of a triangle.

4.1 Classifying Triangles

Legs

Hypotenuse

Base

On a right triangle: sides which form the right angle.

On an isosceles triangle: sides which are congruent.

The longest side on a triangle.

The non-congruent side in an isosceles triangle.

4.1 Classifying Triangles

Adjacent Sides Two sides sharing a common vertex.

4.1 Classifying by Sides

Equilateral

Isosceles

Scalene

Triangles with 3 congruent sides.

Triangle with at least 2 congruent sides.

Triangle with no congruent sides.

4.1 Classifying by Angles

Acute

Equiangular

Right

Obtuse

Triangle with 3 acute angles.

Triangles with 3 congruent angles.

Triangle with one right angle.

Triangle with one obtuse angle.

Sort the last seven terms into two categories:

Classifying By Sides Classifying By Angles

Try it!

• Classifying Triangles (by sides & by angles) with your NEIGHBOR.

• Note that each triangle will have AT LEAST 2 answers.

Closer

• Journal: Why can’t an obtuse triangle have more than one obtuse angle?

Warm UpDec. 22, 2008

• Journal: Classify the triangle by angle and by sides.

60º 60º

Goals Today

• Discuss Classification of Triangles

• Define Triangle Theorems

• Apply Triangle Theorems

4.1 More Vocabulary

Interior Angles

Exterior Angles

1

2 3 4

Angles which are within the triangle.

Angles formed when triangle sides are extended.

4.1 Theorems

Triangle Sum Theorem (Thm. 4.1)

Exterior Angle Theorem (Thm. 4.2)

Corollary to Thm. 4.2

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

The measure of an exterior angle equals the sum of the two non-adjacent interior angles.

The acute angles of a right triangle are complimentary.

Example 1: Classifying Triangles

a) By sides:

By angles:

20º L

23

J 50º 19

110º

K

Example 2: Classifying Triangles

b) By sides:

By angles:

Z

45º

4 5.7

45º

X Y

Example 2: Finding Angle Measures

a) Find the value of x.

(4x-5)º

(3x+11)º

Example 2: Finding Angle Measures

b) Find the value of y.

2yº

50º

On your own: Exercises.

• # 1-5 all. Ask for help if you need it!

With a Neighbor…

• 4.1 Practice A

Closer

• Homework: “Interior and Exterior Angles”

• Journal: When would you have an acute exterior angle?

Warm UpDec. 23, 2009

• Homework Check (Interior and Exterior Angles)

• Journal: Find the value of x.

3xº 30º

2xº

In Congruent Triangles, Order Matters

• ΔABC = ΔDEF

D

A

E F

B C

Goals Today

• Corresponding Triangle Parts

• http://www.youtube.com/watch?v=fks_6d1prC8&feature=fvw

Closer

• Journal: Fill in the missing angles:

60º ?

30º

50º ? ?