Geometry 8-6a GeoGebra Primer: Law of Cosines

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.

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Vocabulary: What is segment h?

A midsegment of △ABC.

An altitude of △ABC.

A median of △ABC.

A perpendicular bisector of segment AB.

10

The same applet is embedded multiple times throughout this activity for convenience as you respond to the items that follow.

10

Exploration: Write an equation that expresses the relationship among A, x, and b.

10

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)

10

Exploration: Write an equation that expresses the relationship among b, x, and h.

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Exploration: Without introducing a new variable, write an equation that expresses the relationship among the sides of △BDC.

Check-up: The expanded form of the equation you selected in the previous item looks like this.

If it does not, reconsider your selection.

10

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

10

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

10

Exploration: In item 4, you found that x = bcos(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

10

Exploration: In item 5, you found that b² = h² + x². 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

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.

Geometry 8-6a GeoGebra Primer: Law of Cosines

Vocabulary: What is segment h?

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.

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?

Exploration: The equation in the previous item can be re-written in this form. Which property justifies this?

Exploration: In item 4, you found that x = bcos(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?

Exploration: In item 5, you found that b² = h² + x². Therefore, the equation in the previous item can be written as follows.Which property justifies this?

Vocabulary: What is segment h?

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.

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?

Exploration: The equation in the previous item can be re-written in this form. Which property justifies this?

Exploration: In item 4, you found that x = bcos(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?

Exploration: In item 5, you found that b² = h² + x². Therefore, the equation in the previous item can be written as follows.Which property justifies this?

Exploration: The expanded equation above can be re-written as follows.
Which property justifies this?

Exploration: The equation in the previous item can be re-written in this form.
Which property justifies this?

Exploration: In item 4, you found that x = bcos(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?

Exploration: In item 5, you found that b² = h² + x². Therefore, the equation in the previous item can be written as follows.
Which property justifies this?

Exploration: The expanded equation above can be re-written as follows.
Which property justifies this?

Exploration: The equation in the previous item can be re-written in this form.
Which property justifies this?

Exploration: In item 4, you found that x = bcos(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?

Exploration: In item 5, you found that b² = h² + x². Therefore, the equation in the previous item can be written as follows.
Which property justifies this?