PSA2QX9 - Classwork---Geometry, M1, Lesson 9 (G.CO.9)

One of the main goals in studying geometry is to develop your ability to reason critically, to draw valid conclusions based upon observations and proven facts. Master detectives do this sort of thing all the time. Take a look as Sherlock Holmes uses seemingly insignificant observations to draw amazing conclusions.

Watch "Sherlock Holmes, Master of Deduction Does it Again" at this link: https://www.youtube.com/watch?v=o30UY_flFgM&feature=youtu.be

Discuss the connection between Holmes’s process of identifying the attacker and the deduction used in geometry.

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Part A)

You know that angles on a line sum to 180°.

Prove that vertical angles are equal in measure.

Make a plan: What do you know about  and  and

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Select one:
Part B)

What conclusion can you draw based on both pieces of knowledge?

Part C)

Write your proof on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Proof is on paper."

Given the diagram, prove that .

Make a plan first. What do you know about , , and ?)

Write your proof on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Proof is on paper."

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Given the diagram to the right, prove .

Write your proof on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Proof is on paper."

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In the diagram, prove that .

(You need to write a label in the diagram that is not labeled yet for this proof.)

Draw your labeled diagram and proof on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work, type "Diagram and proof is on paper."

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In the figure to the right,  and

Prove that .

Write your proof on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Proof is on paper."

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In the figure to the right, prove that the sum of the angles marked by arrows is .

(You need to write several labels in the diagram for this proof.)

Draw your diagram on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Diagram is on paper."

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In the figure to the right, prove that

Draw in label .

Draw your diagram and proof on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Diagram and proof is on paper."

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