F5 Ch6 Finding the Angle Between Two Intersecting Planes

F5 Ch6

Angle Between Two Intersecting Planes

Angle Between Two Intersecting Planes

Material:

A transparent plastic layer

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Instruction:

1. Draw a straight line to connect any two vertices of the given layer

2. Fold the plastic layer to connect the chosen vertices

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​Discuss with your partner:

Now, the folding lines should separate the plastic layer to two planes​.

Where is the angle between the planes? Any conditions behind?​

​Textbook p.11

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Draw

The figure shows a right triangular prism ABCFED.

On the figure, draw the angle between planes ABDE and CBDF.

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Fill in the Blanks

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Mini Summary

​To identify the angle between two intersecting planes, consider

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-Any right-angled triangles?

-Any isosceles triangles or equilateral triangles? (Properties è perpendicular bisectors)

-Any points need to be added? (e.g. Let M be the mid-point of AB)

-Any points need to be connected?

Mini Summary

To find the unknown angles/ sides

For right-angled triangles, consider

1. Pyth. Theorem

2. sin⁡θ, cos⁡θ, tan⁡θ

3. Area of triangles

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Otherwise, consider

1. Sine Formula

2. Cosine Formula

3. Area of triangles (1/2 absin⁡C or Herons’ Formula)