7.4a: The Dot Product

Objectives:

• Find the dot product of two vectors and use the Properties of the Dot Product.

• Find the angle between two vectors and determine whether two vectors are orthogonal.

Definitions & Formulas:

• Dot Product

• Orthogonal

• Properties of the Dot Product

• Angle Between Two Vectors

Examples:

Ex1. Finding the Dot Product (+ student example 1)


Ex2. Properties of the Dot Product (+student example 2)


Ex3. Angle Between Two Vectors


student example 3


Ex4. Orthogonal Vectors


student example 4


Problem set 7.4a 

#2-14 even

26-30 even

36, 48

3.3: Proving Lines Parallel

Objectives:

• Use transversals in proving lines parallel.

Example 1

Student example 1

Example 2

Student example 2

Problem set 3.3

#1-13

3.2: Parallel Lines

Objectives:

• Define Transversal.
• Prove and apply theorems about parallel lines.

Example 1


Student Example 1


Example 2


Student Example 2


Problem Set 3.2:
#1-16

3.1: Proving Angles Congruent

Objectives:

• Use formal methods of proof to show angles congruent.

Example 1 and Student Example 1

*UPDATE: the answer is incorrect. It should be x = 20

Example 2

Student Example 2

Example 3 and Student Example 3

Problem set 3.1

#1-13 all

2.7: Composition of Reflections

Objectives:

• Transform figures by applying a composition of reflections.

Example 1


Example 2


Student Example 1


Problem set 2.7 (in class)
# 1-8, 14-17

2.6: Dilations

Objectives:

• Locate dilation images of figures.

Example 1


Example 2


Student Example 1


Example 3


Student Example 2


Problem set 2.6:
#  1-15

2.4: Rotations

Objectives:

• Draw and identify rotation images of figures.

Quadrantal  rotations chart:

Example 1 & Student Example 1


Example 2 & Student Example 2


Problem set 1.4 (in class):
#1-13 all