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Geometry 8-6a GeoGebra Primer: Law of Cosines
By Matthew Richardson
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Last updated about 4 years ago
10 questions
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Interact with the embedded GeoGebra applet before responding to the items that follow.
Make sure that the black slider has been slid all the way to the right before responding to the questions.
Question 1
1.
The same applet is embedded multiple times throughout this activity for convenience as you respond to the items that follow.
Question 3
3.
Question 4
4.
Question 5
5.
Question 6
6.
Check-up:
The expanded form of the equation you selected in the previous item looks like this.
If it does not, reconsider your selection.
Question 7
7.
Question 8
8.
Question 9
9.
Question 10
10.
Discovery:
This equation is one form of the
Law of Cosines.
The Law of Cosines can be used to identify unknown parts of non-right triangles.
Vocabulary:
What is segment
h
?
A midsegment of △
ABC
.
An altitude of △
ABC
.
A median of △
ABC
.
A perpendicular bisector of segment
AB.
Exploration:
Write an equation that expresses the relationship among
A, x,
and
b
.
Exploration:
Rewrite the equation from the previous item so that
x
is in terms of
A
and
b
.
x = bcos(A)
x = b / cos(A)
x = b / sin(A)
Exploration:
Write an equation that expresses the relationship among
b
,
x
, and
h
.
Exploration:
Without introducing a new variable, write an equation that expresses the relationship among the sides of △
BDC
.
Exploration:
The expanded equation above can be re-written as follows.
Which property justifies this?
Reflexive Property of Equality
Commutative Property of Addition
Substitution Property of Equality
Identity Property of Multiplication
Exploration:
The equation in the previous item can be re-written in this form.
Which property justifies this?
Reflexive Property of Equality
Commutative Property of Addition
Substitution Property of Equality
Identity Property of Multiplication
Exploration:
In item 4, you found that
x
=
b
cos(
A
). Therefore, the equation in the previous item can be written as follows.
In addition to the Commutative Property of Multiplication, which property justifies this?
Reflexive Property of Equality
Commutative Property of Addition
Substitution Property of Equality
Identity Property of Multiplication
Exploration:
In item 5, you found that
b
²
= h
² +
x
². Therefore, the equation in the previous item can be written as follows.
Which property justifies this?
Reflexive Property of Equality
Commutative Property of Addition
Substitution Property of Equality
Identity Property of Multiplication
